Method and apparatus for heating a gas-solvent solution

ABSTRACT

This invention provides a method of quickly heating a gas-solvent solution from a relatively low temperature T1 to a relatively high temperature T2, such that the gas-solvent solution has a much higher dissolved gas concentration at temperature T2 than could be achieved if the gas-solvent solution had originally been formed at the temperature T2. Various apparatuses are also provided for carrying out the heating method.

[0001] This invention claims priority from provisional patentapplication No. 60/287,157, filed in the United States Patent andTrademark Office on Apr. 26, 2001, entitled METHOD AND APPARATUS FORHEATING, by inventor David G. Boyers.

[0002] Prior patent application Ser. No. 09/693,012, filed Oct. 19,2000, “A Method and Apparatus for Treating a Substrate with anOzone-Solvent Solution”, by inventors Boyers and Cremer is herebyincorporated by reference. That patent application is based uponprovisional patent application No. 60/160,435, filed Oct. 19, 1999, “AMethod of Oxidizing Materials at High Speed Using a Solution of OzoneGas Dissolved in Water,” by inventors Boyers and Cremer.

BACKGROUND AND-CROSS-REFERENCE TO RELATED APPLICATIONS

[0003] This invention concerns a method and apparatus for quicklyheating a gas-solvent solution, and particularly an ozone-solventsolution. The method may be used for removing photoresist, post ashphotoresist residue, post-etch residue, and other organic materials fromsemiconductor wafers, flat panel display substrates, and the like athigh speed using a solution of gas dissolved in a solvent, such as ozonedissolved in water.

[0004] Reference

[0005] U.S. Pat. No. 6,037,574, by Lanham, C. C.; Ptasienski, K.;Steinhauser, L. P.; Lake, R. H.; Kreisel, J. H., entitled QUARTZSUBSTRATE HEATER, filed Nov. 6, 1997, issued Mar. 14, 2000.

SUMMARY OF INVENTION

[0006] This invention provides a method of quickly heating anozone-solvent solution from a relatively low temperature T1 to arelatively high temperature T2, such that the ozone-solvent solution hasa much higher dissolved ozone concentration at temperature T2 than couldbe achieved if the ozone-solvent solution had originally been formed atthe temperature T2. The method includes the steps of:

[0007] a) introducing the ozone-solvent solution at a temperature T1into a heating volume;

[0008] b) transferring sufficient power into the heating volume whilethe ozone-solvent solution is flowing through the heating volume tocreate a heated flowing ozone-solvent solution having a temperature T2at the outlet orifice of the heating volume, and

[0009] c) receiving the heated flowing ozone-solvent solution at theoutlet orifice of the heating volume.

[0010] Various apparatuses are also provided for carrying out theheating method. In the preferred mode, the fluid is heated at high speedby using a heated volume that is relatively small, in order to minimizethe residence time of the fluid inside the heated volume at a given flowrate to minimize the time required to increase the temperature of thefluid from T1 to T2.

[0011] Features and Advantages

[0012] can be implemented in a high-purity metal free design: provides amethod and apparatus for quickly heating a flowing ozone-solventsolution which avoids the introduction of metals or other contaminantsinto the ozone-solvent solution.

[0013] extremely small residence volume: provides a method and apparatusfor quickly heating a flowing ozone-solvent solution with a very smallresidence volume so as to minimize the time required for the solution tomove from its initial unheated state at the heater inlet to its heatedstate at the heater outlet.

[0014] can be manufactured using existing materials and technology:provides an apparatus for quickly heating a flowing ozone-solventsolution which can readily manufactured using existing materials andtechnology.

[0015] high reliability: provides an apparatus for heating which canmeet the reliability requirements for equipment used in a manufacturingoperation.

BRIEF DESCRIPTION OF DRAWINGS

[0016] The various features of the present invention and its preferredembodiments may be better understood by referring to the followingdiscussion and the accompanying drawings in which like referencenumerals refer to like elements in the several figures. The contents ofthe following discussion and the drawings are set forth as examples onlyand should not be understood to represent limitations upon the scope ofthe present invention.

[0017] 1st GROUP: Direct Conduction Heater Designs (FIG. 1 and FIG. 2)

[0018] 2^(nd) GROUP: Heat Exchanger Designs (FIG. 3 and FIG. 4)

[0019] 3^(rd) GROUP: Direct Microwave Heater Designs (FIG. 5)

[0020] 4^(th) GROUP: Direct Infrared Heater Designs (FIG. 6)

[0021] 5th GROUP: Heated Fluid Injection Designs (FIG. 7)

[0022] 6^(th) GROUP: Long Heater Design Geometry (FIG. 8 and FIG. 9)

[0023] Direct Conduction Heater Designs

[0024]FIG. 1. illustrates a single tube resistance heated designemploying a tube with resistive heating elements in thermal contact withthe outer surface of the tube. The fluid to be heated (process fluid)flows through the tube.

[0025]FIG. 2. illustrates a single tube induction heated designemploying a tube with inductively heated elements in thermal contactwith the outer surface of the tube. The fluid to be heated (processfluid) flows through the tube.

[0026] Heat Exchanger Designs

[0027]FIG. 3. illustrates a single tube-in-tube heat exchanger with aheated fluid (working fluid) flowing in the volume between the outertube and the inner tube and the fluid to be heated (process fluid)flowing through the inner tube.

[0028]FIG. 4. illustrates a multiple tube-in-tube heat exchanger with aheated fluid (working fluid) flowing in the volume between the outertube and the multiplicity of inner tubes and the fluid to be heated(process fluid) flowing through the inner tubes.

[0029] Direct Microwave Heater Design

[0030]FIG. 5. illustrates a single tube microwave heated designemploying a liquid carrying conduit inside a microwave resonatorconnected to microwave power source to heat the liquid flowing in theliquid carrying conduit. The fluid to be heated (process fluid) flowsthrough the tube.

[0031] Direct Infrared Heater Design

[0032]FIG. 6. illustrates a single tube infrared heated design employinga liquid carrying conduit with minimal infrared absorption and anadjacent infrared radiation source to heat the liquid flowing in theliquid carrying conduit. The fluid to be heated (process fluid) flowsthrough the tube.

[0033] Heated Fluid Injection Design

[0034]FIG. 7. illustrates a fluid injection type heater with a heatedfluid (heated water or steam for example) injected into the inlet portof an injector and the fluid to be heated (cold process fluid) flowinginto the motive flow inlet of the injector and the heated process fluidflowing from the outlet port of the injector.

[0035] Long Heater Design Geometry

[0036]FIG. 8 illustrates a general approach to joining individualstraight sections of heater with fittings into a folded compact heaterdesign.

[0037]FIG. 9 illustrates a general approach to bending a long heaterinto a coil for a compact heater design.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0038] TABLE 1 Example Direct Conduction Heater Designs Heating MethodHeat Source Wetted Geometry Figure Direct Conduction Heater Single Tube(ST), Resistance ®, Single Tube-in- Induction (I), Teflon (T), Tube(STT), or Microwave or Multiple Tube-in- (MW) Quartz (Q) Tube (MTT) R QST 1 R Q STT R Q MTT R T ST 1 R T STT R T MTT I Q ST 2 I Q STT I Q MTT IT ST 2 I T STT I T MTT

[0039] TABLE 2 Example Heat Exchanger Designs Heating Method Wetted HeatSource Material Geometry Figure Heat Exchanger Heated Liquid StainlessSingle Tube-in- (HL), Steam Steel (SS), Tube (STT), (S), or HeatedTeflon (T), Multiple Tube-in- Gas (HG) or Quartz (Q) Tube (MTT) HL SSSTT 3 HL SS MTT 4 HL T STT 3 HL T MTT 4 HL Q STT 3 HL Q MTT 4 S SS STT 3S SS MTT 4 S Q STT 3 S Q MTT 4 HG SS STT 3 HG SS MTT 4 HG Q STT 3 HG QMTT 4

[0040] TABLE 3 Example Microwave Heater Designs Heating Method WettedGeometry Figure Heat Source Material Geomery Figure Direct MicrowaveHeater Teflon (T), Microwave or (MW) Quartz (Q) Single Tube (ST), MWRadiation Q ST 5 MW Radiation T ST 5

[0041] TABLE 4 Example Infrared Heater Designs Heating Method HeatSource Wetted Material Geometry Figure Direct Infrared Heater InfraredQuartz (Q) Single Tube (ST), Infrared Q ST 6 Radiation

[0042] TABLE 5 Example Heated Fluid Injection Designs Heating MethodHeat Source Wetted Material Geometry Figure Heated Fluid InjectionHeated Liquid Stainless Steel Single Tube w/ (HL) or Steam (SS), Teflon(T), Injector (S) or Quartz (Q) (STI) S SS STI 7 S T STI 7 S Q STI 7 HLSS STI 7 HL T STI 7 HL Q STI 7

[0043] Heater Design—Technical Approach

[0044] Given the temperature and flow rate of the liquid entering theheater and the desired outlet temperature, we can compute the energythat must be transferred to the liquid by the heater. In the case inwhich the liquid to be heated is water, we can make such a calculation.The results are shown in Table 6 below. TABLE 6 Point-of-use HeaterPower Requirement Dispense Flow Inlet Water Desired Outlet Required RateTemp. Water Temp. Temp. Increase Power (L/min) (deg. C.) (deg. C.) (deg.C.) Req'd (kW) 2.7 5 45 40 7.45 2.7 5 55 50 9.3 2.7 5 65 60 11.2 2.7 575 70 13.0 2.7 5 85 80 14.9 2.7 5 95 90 16.8 3.3 5 45 40 9.1 3.3 5 55 5011.4 3.3 5 65 60 13.7 3.3 5 75 70 15.9 3.3 5 85 80 18.2 3.3 5 95 90 20.5

[0045] We can heat the flowing liquid by transferring heat from aresistance heating element or induction heated element in thermalcontact with the outer surface of a tube carrying the liquid. The energythat can be transferred is directly proportional to the averagetemperature difference between the flowing liquid and the heated elementand the thermal resistance between the flowing liquid and the heatingelements. The thermal resistance is the sum of the thermal resistancebetween the flowing liquid and the inner surface of the tube carryingthe liquid and the thermal resistance from the inner surface of the tubeto the heating element on the outer surface of the tube. The firstresistance is lower at higher flow rates where the Reynolds number ishigher and the boundary layer thickness is smaller and the secondresistance is lower for tubes with thin walls made from materials withhigh thermal conductivity. The thermal resistance is also made smallerif the area through which the energy is transferred is larger. When thesurface area is made larger by increasing the length of the tube, thenthe pressure drop from the tube inlet to tube outlet (fluid flowresistance) increases. If the surface area is made larger by increasingthe diameter of the tube, then the pressure fluid velocity and pressuredrop for a given flow rate is lower. However, the lower flow velocityproduces a lower Reynolds number and high thermal resistance (filmresistance) between the flowing liquid and the inner surface of thetube. If the liquid is carried by a multiplicity of small diametertubes, then the surface area will be larger than a design in which thesame flow is carried by a single tube of the same cross sectional area.

[0046] Whereas the use of tube materials of high thermal conductivitywill reduce the temperature difference required to transfer a givenamount of energy for a given surface area, the choice of materials canbe limited by the materials compatible with the particular application.Whereas metals such as 316 stainless steel can be used in someapplications, other applications may not use metals. In many high purityapplications such as semiconductor manufacturing, the wetted materialsare materials such as quartz, Teflon PFA, Teflon PTFE. These materialshave a lower thermal conductivity than metals (See Table 7 below).Accordingly, if a resistance heated or induction heated heater or fluidto fluid heat exchanger is to transfer a given amount of energy at agiven temperature difference using these lower thermal conductivitymaterials, then the material area can be made relatively large for agiven material thickness. TABLE 7 Thermal Conductivity Data MaterialThermal Conductivity (watt/meter deg. K) 316 Stainless Steel 16.3Titanium 16.3 Quartz 1.4 Teflon PTFE 0.245

[0047] We have made some sample calculations of the required temperaturedifference to transfer 9,000 watts for the several heater designs for aprocess fluid inlet temperature of 20 degree C. and flow rate of 2.65L/min. These are shown in the spread sheet below. We can see that adesign using a 10 foot length of 0.250 inch OD, 0.180 inch ID 316stainless steel tubing heated on the exterior can transfer 9 Kwatt towater flowing through the tubing at a flow rate of 2.65 L/min bymaintaining a maximum and minimum element temperature on the exteriorwall of the tube of only about 46 and 95 degree C., respectively asshown under design example 1. When the tube wall is made from quartz, aheater of the same dimensions can transfer the same power to the flowingwater if the maximum and minimum element temperature on the exteriorwall of the tube is increased to 46 and 95 degree C., respectively asshown under design example 2. If the heater length is increased to 15 or20 feet, then the exterior temperatures can be reduced further whilelimiting the internal volume to no more than 100 ml as shown in designexample 3 and 4. This is contrasted with a conventional designresistance heated quartz tube heater. Such a heater has very lowreynolds numbers and therefore very high thermal resistance between theflowing water and the inner surface of the tube and very thick wall andtherefore a very high thermal resistance from the inside wall to theoutside wall. Accordingly, a 1.75 inch OD, 1.5625 ID, 27 inch longheater will transfer the 9 Kw to the flowing stream if the maximum andminimum element temperature on the exterior wall of the tube isincreased to 584 and 619 degree C., respectively, as shown under theconventional design example. These element temperatures are much higherthan required for the designs in examples 2, 3,and 4. (See Table 8)

[0048] Direct Conduction Heater Design Calculations TABLE 8 Heaterdesign performance calculations - applicable to tube heaters withresistance heated or induction heated elements bonded to the surface lowvolume, high performance Inventive Inventive Inventive Inventive PriorArt heater design Design A Design B Design C Design D Design tubing ID(inches) 0.18 0.18 0.18 0.18 1.5625 tubing OD (inches) 0.25 0.25 0.250.25 1.75 tubing wall thickness (inches) 0.035 0.035 0.035 0.035 0.09375tubing ID (cm) 0.457 0.457 0.457 0.457 3.969 tubing OD (cm) 0.635 0.6350.635 0.635 4.445 tubing wall thickness (cm) 0.089 0.089 0.089 0.0890.238 length of heated tube (in) 120.00 120.00 180.00 240.00 27.00length of heated tube (cm) 304.8 304.8 457.2 609.6 68.6 volume of heatedtube (cm3) = ml 50.0 50.0 75.1 100.1 848.4 liquid fluid material beingheated water water water water water fluid inlet temperature (deg. C.)20 20 20 20 20 fluid density rho (g/cm3) 0.9974 0.9974 0.9974 0.99740.9974 fluid kinematic viscosity eta 9.80E−03 9.80E−03 9.80E−03 9.80E−039.80E−03 (g/cm-sec) flow rate (gal/min) 0.7 0.7 0.7 0.7 0.7 flow rate(liters/min) 2.65 2.65 2.65 2.65 2.65 flow rate (ml/sec) 44.16 44.1644.16 44.16 44.16 tubing flow cross section area 0.1642 0.1642 0.16420.1642 12.3708 (cm2) free stream velocity through tubing 269.00 269.00269.00 269.00 3.57 (cm/sec) Re = density * free stream 12517 12517 1251712517 1442 vel. * hydraulic.diam/kinem. viscosity nozzle ID frictionfactor (turbulent 0.0295 0.0295 0.0295 0.0295 0.0592 flow - FIG. 6.4)pressure drop across tubing 71087.29 71087.29 106630.93 142174.58 0.65(newtons/m2) Pascal pressure drop across tubing (psi) 10.31 10.31 15.4620.62 0.00 fluid residence time at flow rate 1.13 1.13 1.70 2.27 19.21(secs) Prandtl Number Pr for water at 20 6.78 6.78 6.78 6.78 6.78 deg C.(dimensionless) = Cp * viscosity/k Nusselt No. 93.80 93.80 93.80 93.8016.65 Nu = 0.023R{circumflex over ( )}0.8 * Pr{circumflex over ( )}0.4,turbulent flow thermal conductivity of water at 20 0.00604 0.006040.00604 0.00604 0.00604 deg. C. watt/cm/deg C. heat transfer coefficient1.24 1.24 1.24 1.24 0.03 watt/cm2/deg. C. normalized film resistance(tube 0.807 0.807 0.807 0.807 39.467 inner wall to water) (degC./watt/cm2) tube inner surface area (cm2) 437.8 437.8 656.7 875.6 855.1tube outer surface area (cm2) 608.0 608.0 912.1 1216.1 957.7 thermalresistance from water to 0.00184 0.00184 0.00123 0.00092 0.04616 tubeinner surface (deg. C./watt) percent of total thermal resistance - 64%13% 13% 13% 71% water to tube thickness of tube wall (cm) 0.089 0.0890.089 0.089 0.238 tubing material 316L QUARTZ QUARTZ QUARTZ QUARTZ tubematerial thermal conductivity 0.163 0.014 0.014 0.014 0.014(watt/cm-deg. C.) normalized thermal resistance 0.55 6.35 6.35 6.3517.01 through the tube wall (deg C./watt/cm2) average area of tube wall(cm2) 523 523 784 1,046 906 thermal resistance through the tube 0.001040.01214 0.00810 0.00607 0.01877 wall (deg C./watt) percent of totalthermal resistance - 36% 87% 87% 87% 29% tube wall total thermalresistance (deg 0.00289 0.01399 0.00932 0.00699 0.06492 C./watt) total(normalized to external 1.75 8.50 8.50 8.50 62.17 surface) thermalresistance (deg C./watt/cm2) Power (watt) 9000 9000 9000 9000 9000 massflow rate of water (grams/sec) 44 44 44 44 44 heat capacity of water4.179 4.179 4.179 4.179 4.179 Joules/gram/deg. C. temperature rise ofwater from inlet 48.89 48.89 48.89 48.89 48.89 to outlet (deg. C.)Power Density-Tube Exterior 14.80 14.80 9.87 7.40 9.40Surface (watts/cm2) Power Density - Tube Exterior 95.49 95.49 63.6647.75 60.63 (watts/in2) Aveage Fluid Temperature (inlet 34.45 34.4534.45 34.45 34.45 and outlet) Temp.Diff. to Transfer Specified 25.98125.88 83.92 62.94 584.30 Power (deg. C.) Average Element Temp. =Exterior 60.42 160.32 118.37 97.39 618.75 Surface Temp. to Transfer SpecPower (deg. C.) minimum element temperature 45.98 145.88 103.92 82.94604.30 (deg. C.) maximum element temperature 94.87 194.77 152.81 131.83653.19 (deg. C.)

[0049] Complete Heater Design Examples—Inventive Examples Compared toPrior Art TABLE 9 Example 1 - Inventive Example Inventive Example for2.5 L/min flow tubing ID (inches) (lNPUT DATA) 0.18 0.18 0.18 0.18 0.180.18 tubing OD (inches) (INPUT DATA) 0.25 0.25 0.25 0.25 0.25 0.25Inlet Temp T1 deg. C. (INPUT 5 5 5 5 5 5 DATA)Outlet Temp T2 deg. C. (INPUT 35 40 45 50 60 70 DATA) Req'd TemperatureRise deg. C. 30 35 40 45 55 65 Flow Rate L/min (INPUT DATA) 2.5 2.5 2.52.5 2.5 2.5 Flow Rate ml/sec 41.67 41.67 41.67 41.67 41.67 41.67Req'd Power kW 5.19 6.05 6.91 7.78 9.51 11.23Decay Constant Tau sec for given 79.4 52.9 35.7 24.3 11.7 5.9ozone-water solution temp.T2 tubing ID (inches) 0.18 0.18 0.18 0.18 0.180.18 tubing OD (inches) 0.25 0.25 0.25 0.25 0.25 0.25 tubing wallthickness (inches) 0.035 0.035 0.035 0.035 0.035 0.035 tubing ID (cm)0.457 0.457 0.457 0.457 0.457 0.457 tubing OD (cm) 0.635 0.635 0.6350.635 0.635 0.635 tubing wall thickness (cm) 0.089 0.089 0.089 0.0890.089 0.089 length of heated tube (in) scaled for 111.11 129.63 148.15166.67 203.70 240.74 given surf.pwr. density length of heated tube (ft)9.26 10.80 12.35 13.89 16.98 20.06 length of heated tube (cm) 282.2329.3 376.3 423.3 517.4 611.5 volume of heated tube (cm3) = ml 46.3 54.161.8 69.5 84.9 100.4 liquid fluid material being heated water waterwater water water water fluid inlet temperature (deg. C.) 5 5 5 5 5 5fluid density rho (g/cm3) 0.9974 0.9974 0.9974 0.9974 0.9974 0.9974fluid kinematic viscosity eta (g/cm- 9.80E−03 9.80E−03 9.80E−03 9.80E−039.80E−03 9.80E−03 sec) flow rate (liters/min) 2.50 2.50 2.50 2.50 2.502.50 flow rate(ml/sec) 41.67 41.67 41.67 41.67 41.67 41.67 tubing flowcross section area (cm2) 0.1642 0.1642 0.1642 0.1642 0.1642 0.1642 freestream velocity through tubing 253.80 253.80 253.80 253.80 253.80 253.80(cm/sec) Re = density * free stream 11810 11810 11810 11810 11810 11810vel. * hydraulic.diam/kinem. viscosity nozzle ID friction factor(turbulent 0.0300 0.0300 0.0300 0.0300 0.0300 0.0300 flow-FIG. 6.4)pressure drop across tubing 59528 69450 79371 89292 109135 128978(newtons/m2) Pascal pressure drop across tubing (psi) 8.63 10.07 11.5112.95 15.82 18.70 fluid residence time at flow rate 1.11 1.30 1.48 1.672.04 2.41 (secs) Prandtl No. Pr for water at 20 deg 6.78 6.78 6.78 6.786.78 6.78 C. = Cp * viscos/k (dimensionless) Nusselt No. Nu =0.023Re{circumflex over (0.8 )}* Pr{circumflex over (0.4,)} 89.54 89.5489.54 89.54 89.54 89.54 turbulent flow thermal conductivity of water at20 .00604 .00604 .00604 .00604 .00604 .00604 deg. C. watt/cm/deg C. heattransfer coefficient 1.18 1.18 1.18 1.18 1.18 1.18 watt/cm2/deg. C.normalized film resis. (tube inner 0.845 0.845 0.845 0.845 0.845 0.845wall to water) (deg C./watt/cm2) tube inner surface area (cm2) 405.4472.9 540.5 608.0 743.2 878.3 tube outer surface area (cm2) 563.0 656.8750.7 844.5 1032.2 1219.9 thermal resistance from water to tube .00209.00179 .00156 .00139 .00114 .00096 inner surface (deg. C./watt) percentof total thermal resistance - 14% 14% 14% 14% 14% 14% water to tubethickness of tube wall (cm) 0.089 0.089 0.089 0.089 0.089 0.089 tubingmaterial QRTZ QRTZ QRTZ QRTZ QRTZ QRTZ tube material thermalconductivity 0.014 0.014 0.014 0.014 0.014 0.014 (watt/cm-deg. C.)normalized thermal resis. through the 6.35 6.35 6.35 6.35 6.35 6.35 tubewall (deg C./watt/cm2) average area of tube wall (cm2) 484 565 646 726888 1,049 thermal resistance through the tube .01311 .01124 .00984.00874 .00715 .00605 wall (deg C./watt) percent of total thermalresistance - 86% 86% 86% 86% 86% 86% tube wall total thermal resistance(deg C./watt) .01520 .01303 .01140 .01013 .00829 .00702 total(normalized to ext. surf.) therm. 8.56 8.56 8.56 8.56 8.56 8.56resist.(deg C./watt/cm2) Transferred Power (watt) 5185 6049 6914 77789506 11235 Transferred Volume Power Density 112 112 112 112 112 112(watt/cm3) mass flow rate of water (grams/sec) 42 42 42 42 42 42 heatcapacity of water 4.179 4.179 4.179 4.179 4.179 4.179 Joules/gram/deg.C. temperature rise of water from inlet 29.86 34.83 39.81 44.78 54.7464.69 to outlet (deg. C.) Surface Power Density-Tube Exterior 9.21 9.219.21 9.21 9.21 9.21 Surface (watts/cm2) Surface Power Density - Tube59.42 59.42 59.42 59.42 59.42 59.42 Exterior (watts/in2) Aveage FluidTemperature (inlet and 17.43 19.92 22.40 24.89 29.87 34.84 outlet) Temp.Diff. to Transfer Specified 78.82 78.82 78.82 78.82 78.82 78.82 Power(deg. C.) Avg. Element Temp. = Ext. Surf. 96.24 98.73 101.22 103.71108.68 113.66 Temp. to XFR Spec Pwr. (deg. C.) minimum elementtemperature (deg. C.) 83.82 83.82 83.82 83.82 83.82 83.82maximum element temperature (deg. C.) 113.67 118.65 123.62 128.60 138.55148.50 outlet diss. ozone concentration/inlet 0.99 0.98 0.96 0.93 0.840.67 diss. ozone concentration

[0050] TABLE 10 Example 2 - Inventive Example Inventive Example for 5.0L/min flow tubing ID (inches) 0.305 0.305 0.305 0.305 0.305 0.305tubing OD (inches) 0.375 0.375 0.375 0.375 0.375 0.375Inlet Temp T1 deg. C. 5 5 5 5 5 5 Outlet Temp T2 deg. C. 35 40 45 50 6070 Req'd Temperature Rise deg. C. 30 35 40 45 55 65 Flow Rate L/min 5 55 5 5 5 Flow Rate ml/sec 83.3 83.3 83.3 83.3 83.3 83.3 Reg' d Power kW10.37 12.10 13.83 15.56 19.01 22.47 Decay Constant Tau sec for given79.4 52.9 35.7 24.3 11.7 5.9 ozone-water solution temp.T2tubing ID (inches) 0.305 0.305 0.305 0.305 0.305 0.305tubing OD (inches) 0.375 0.375 0.375 0.375 0.375 0.375 tubing wallthickness (inches) 0.035 0.035 0.035 0.035 0.035 0.035 tubing ID (cm)0.775 0.775 0.775 0.775 0.775 0.775 tubing OD (cm) 0.953 0.953 0.9530.953 0.953 0.953 tubing wall thickness (cm) 0.089 0.089 0.089 0.0890.089 0.089 length of heated tube (in) scaled for 75.00 87.50 100.00112.50 137.50 162.50 given surf.pwr. density length of heated tube (ft)6.25 7.29 8.33 9.37 11.46 13.54 length of heated tube (cm) 190.5 222.2254.0 285.7 349.2 412.7 volume of heated tube (cm3) = ml 89.8 104.8119.7 134.7 164.6 194.6 liquid fluid material being heated water waterwater water water water fluid inlet temperature (deg. C.) 5 5 5 5 5 5fluid density rho (g/cm3) 0.9974 0.9974 0.9974 0.9974 0.9974 0.9974fluid kinematic viscosity eta (g/cm- 9.80E−03 9.80E−03 9.80E−03 9.80E−039.80E−03 9.80E−03 sec) flow rate (liters/min) 5.00 5.00 5.00 5.00 5.005.00 flow rate (ml/sec) 83.33 83.33 83.33 83.33 83.33 83.33 tubing flowcross section area (cm2) 0.4714 0.4714 0.4714 0.4714 0.4714 0.4714 freestream velocity through tubing 176.79 176.79 176.79 176.79 176.79 176.79(cm/sec) Re = density * free stream 13939 13939 13939 13939 13939 13939vel. * hydraulic.diam/kinem. viscosity nozzle ID friction factor(turbulent 0.0287 0.0287 0.0287 0.0287 0.0287 0.0287 flow - FIG. 6.4)pressure drop across tubing 11001 12835 14668 16502 20169 23836(newtons/m2) Pascal pressure drop across tubing (psi) 1.60 1.86 2.132.39 2.92 3.46 fluid residence time at flow rate 1.08 1.26 1.44 1.621.98 2.33 (secs) Prandtl No. Pr for water at 20 deg 6.78 6.78 6.78 6.786.78 6.78 C. = Cp * viscos/k (dimensionless) Nusselt No. Nu =0.023Re{circumflex over ( )}0.8 * Pr{circumflex over ( )}0.4, 102.24102.24 102.24 102.24 102.24 102.24 turbulent flow thermal conductivityof water at 20 .00604 .00604 .00604 .00604 .00604 .00604 deg. C.watt/cm/deg C. heat transfer coefficient 0.80 0.80 0.80 0.80 0.80 0.80watt/cm2/deg. C. normalized film resis. (tube inner 1.255 1.255 1.2551.255 1.255 1.255 wall to water) (deg C./watt/cm2) tube inner surfacearea (cm2) 463.6 540.9 618.2 695.4 850.0 1004.5 tube outer surface area(cm2) 570.0 665.0 760.1 855.1 1045.1 1235.1 thermal resist. from waterto tube .00271 .00232 .00203 .00180 .00148 .00125 inner surface (deg.C./watt) percent of total thermal resistance - 18% 18% 18% 18% 18% 18%water to tube thickness of tube wall (cm) 0.089 0.089 0.089 0.089 0.0890.089 tubing material QRTZ QRTZ QRTZ QRTZ QRTZ QRTZ tube materialthermal conductivity 0.014 0.014 0.014 0.014 0.014 0.014 (watt/cm-deg.C.) normalized thermal resis. through the 6.35 6.35 6.35 6.35 6.35 6.35tube wall (deg C./watt/cm2) average area of tube wall (cm2) 517 603 689775 948 1,120 thermal resistance through the tube .01229 .01053 .00921.00819 .00670 .00567 wall (deg C./watt) percent of total thermalresistance - 82% 82% 82% 82% 82% 82% tube wall total thermal resistance(deg C./watt) .01499 .01285 .01124 .00999 .00818 .00692 total(normalized to ext. surf.) therm. 8.55 8.55 8.55 8.55 8.55 8.55resist.(deg C./watt/cm2) Transferred Power (watt) 10370 12099 1382715556 19012 22469 Transferred Volume Power Density 115 115 115 115 115115 (watt/cm3) mass flow rate of water (grams/sec) 83 83 83 83 83 83heat capacity of water 4.179 4.179 4.179 4.179 4.179 4.179Joules/gram/deg. C. temperature rise of water from inlet 29.86 34.8339.81 44.78 54.74 64.69 to outlet (deg. C.)Surface Power Density-Tube Exterior 18.19 18.19 18.19 18.19 18.19 18.19Surface (watts/cm2) Surface Power Density - Tube 117.37 117.37 117.37117.37 117.37 117.37 Exterior (watts/in2) Aveage Fluid Temperature(inlet and 17.43 19.92 22.40 24.89 29.87 34.84 outlet) Temp.Diff. toTransfer Specified 155.48 155.48 155.48 155.48 155.48 155.48 Power (deg.C.) Avg. Element Temp. = Ext. Surf. 172.90 175.39 177.88 180.37 185.34190.32 Temp. to XFR Spec Pwr. (deg. C.) minimum element temperature(deg. C.) 160.48 160.48 160.48 160.48 160.48 160.48maximum element temperature (deg. C.) 190.33 195.31 200.28 205.26 215.21225.16 outlet diss. ozone concentration/inlet 0.99 0.98 0.96 0.94 0.850.67 diss. ozone concentration

[0051] TABLE 11 Example 3 - Inventive Example Inventive Example for 10.0L/min flow tubing ID (inches) 0.305 0.305 0.305 0.305 0.305 0.305tubing OD (inches) 0.375 0.375 0.375 0.375 0.375 0.375Inlet Temp T1 deg. C. 5 5 5 5 5 5 Outlet Temp T2 deg. C. 35 40 45 50 6070 Req'd Temperature Rise deg. C. 30 35 40 45 55 65 Flow Rate L/min 1010 10 10 10 10 Flow Rate ml/sec 166.7 166.7 166.7 166.7 166.7 166.7Req' d Power kW 20.74 24.20 27.65 31.11 38.02 44.94Decay Constant Tau sec for given 79.4 52.9 35.7 24.3 11.7 5.9ozone-water solution temp.T2 tubing ID (inches) 0.305 0.305 0.305 0.3050.305 0.305 tubing OD (inches) 0.375 0.375 0.375 0.375 0.375 0.375tubing wall thickness (inches) 0.035 0.035 0.035 0.035 0.035 0.035tubing ID (cm) 0.775 0.775 0.775 0.775 0.775 0.775 tubing OD (cm) 0.9530.953 0.953 0.953 0.953 0.953 tubing wall thickness (cm) 0.089 0.0890.089 0.089 0.089 0.089 length of heated tube (in) scaled for 150.00175.00 200.00 225.00 275.00 325.00 given surf.pwr. densitylength of heated tube (ft) 12.50 14.58 16.67 18.75 22.92 27.08 length ofheated tube (cm) 381.0 444.5 508.0 571.5 698.5 825.5volume of heated tube (cm3) = ml 179.6 209.5 239.5 269.4 329.2 389.1liquid fluid material being heated water water water water water waterfluid inlet temperature (deg. C.) 5 5 5 5 5 5 fluid density rho (g/cm3)0.9974 0.9974 0.9974 0.9974 0.9974 0.9974 fluid kinematic viscosity eta(g/cm- 9.80E−03 9.80E−03 9.80E−03 9.80E−03 9.80E−03 9.80E−03 sec) flowrate (liters/min) 10.00 10.00 10.00 10.00 10.00 10.00 flow rate (ml/sec)166.67 166.67 166.67 166.67 166.67 166.67 tubing flow cross section area(cm2) 0.4714 0.4714 0.4714 0.4714 0.4714 0.4714 free stream velocitythrough tubing 353.58 353.58 353.58 353.58 353.58 353.58 (cm/sec) Re =density * free stream 27878 27878 27878 27878 27878 27878 vel. *hydraulic.diam/kinem. viscosity nozzle ID friction factor (turbulent0.0240 0.0240 0.0240 0.0240 0.0240 0.0240 flow - FIG. 6.4) pressure dropacross tubing 73695 85977 98259 110542 135107 159672 (newtons/m2) Pascalpressure drop across tubing (psi) 10.69 12.47 14.25 16.03 19.59 23.15fluid residence time at flow rate 1.08 1.26 1.44 1.62 1.98 2.33 (secs)Prandtl No. Pr for water at 20 deg 6.78 6.78 6.78 6.78 6.78 6.78 C =Cp * viscos/k (dimensionless) Nusselt No. Nu = 0.023Re{circumflex over( )}0.8 * Pr{circumflex over ( )}0.4, 178.01 178.01 178.01 178.01 178.01178.01 turbulent flow thermal conductivity of water at 20 .00604 .00604.00604 .00604 .00604 .00604 deg. C. watt/cm/deg C. heat transfercoefficient 1.39 1.39 1.39 1.39 1.39 1.39 watt/cm2/deg. C. normalizedfilm resis. (tube inner 0.721 0.721 0.721 0.721 0.721 0.721 wall towater) (deg C./watt/cm2) tube inner surface area (cm2) 927.3 1081.81236.3 1390.9 1700.0 2009.1 tube outer surface area (cm2) 1140.1 1330.11520.1 1710.1 2090.1 2470.2 thermal resist. from water to tube .00078.00067 .00058 .00052 .00042 .00036 inner surface (deg. C./watt) percentof total thermal resistance - 11% 11% 11% 11% 11% 11% water to tubethickness of tube wall (cm) 0.089 0.089 0.089 0.089 0.089 0.089 tubingmaterial QRTZ QRTZ QRTZ QRTZ QRTZ QRTZ tube material thermalconductivity 0.014 0.014 0.014 0.014 0.014 0.014 (watt/cm-deg. C.)normalized thermal resis. through the 6.35 6.35 6.35 6.35 6.35 6.35 tubewall (deg C./watt/cm2) average area of tube wall (cm2) 1,034 1,206 1,3781,551 1,895 2,240 thermal resistance through the tube .00614 .00527.00461 .00410 .00335 .00284 wall (deg C./watt) percent of total thermalresistance - 89% 89% 89% 89% 89% 89% tube wall total thermal resistance(deg C./watt) .00692 .00593 .00519 .00461 .00377 .00319 total(normalized to ext. surf.) therm. 7.89 7.89 7.89 7.89 7.89 7.89 resist.(deg C./watt/cm2) Transferred Power (watt) 20741 24198 27654 31111 3802544938 Transferred Volume Power Density 115 115 115 115 115 115(watt/cm3) mass flow rate of water (grams/sec) 166 166 166 166 166 166heat capacity of water 4.179 4.179 4.179 4.179 4.179 4.179Joules/gram/deg. C. temperature rise of water from inlet 29.86 34.8339.81 44.78 54.74 64.69 to outlet (deg. C.) Surface Power Density - TubeExterior 18.19 18.19 18.19 18.19 18.19 18.19 Surface (watts/cm2)Surface Power Density-Tube 117.37 117.37 117.37 117.37 117.37 117.37Exterior (watts/in2) Aveage Fluid Temperature (inlet and 17.43 19.9222.40 24.89 29.87 34.84 outlet) Temp.Diff. to Transfer Specified 143.53143.53 143.53 143.53 143.53 143.53 Power (deg. C.) Avg. Element Temp. =Ext. Surf. 160.96 163.45 165.93 168.42 173.40 178.37 Temp. to XFR SpecPwr. (deg. C.) minimum element temperature (deg. C.) 148.53 148.53148.53 148.53 148.53 148.53 maximum element temperature (deg. C.) 178.39183.36 188.34 193.31 203.27 213.22 outletdiss. ozone concentration/inlet 0.99 0.98 0.96 0.94 0.85 0.67diss. ozone concentration

[0052] TABLE 12 Example 4 - Prior Art Design Prior Art Example for 2.5L/min flow tubing ID (inches) 1.5625 1.5625 1.5625 1.5625 1.5625 1.5625tubing OD (inches) 1.75 1.75 1.75 1.75 1.75 1.75 Inlet Temp T1 deg. C. 55 5 5 5 5 Outlet Temp T2 deg. C. 35 40 45 50 60 70 Req'd TemperatureRise deg. C. 30 35 40 45 55 65 Flow Rate L/min 2.5 2.5 2.5 2.5 2.5 2.5Flow Rate ml/sec 41.7 41.7 41.7 41.7 41.7 41.7 Req'd Power kW 5.19 6.056.91 7.78 9.51 11.23 Decay Constant Tau sec for given 79.4 52.9 35.724.3 11.7 5.9 ozone-water solution temp.T2 tubing ID (inches) 1.56251.5625 1.5625 1.5625 1.5625 1.5625 tubing OD (inches) 1.75 1.75 1.751.75 1.75 1.75 tubing wall thickness (inches) .09375 .09375 .09375.09375 .09375 .09375 tubing ID (cm) 3.969 3.969 3.969 3.969 3.969 3.969tubing OD (cm) 4.445 4.445 4.445 4.445 4.445 4.445 tubing wall thickness(cm) 0.238 0.238 0.238 0.238 0.238 0.238 length of heated tube (in)scaled for 15.56 18.15 20.74 23.33 28.52 33.70 given surf.pwr. densitylength of heated tube (ft) 1.30 1.51 1.73 1.94 2.38 2.81 length ofheated tube (cm) 39.5 46.1 52.7 59.3 72.4 85.6volume of heated tube (cm3) = ml 488.8 570.2 651.7 733.2 896.1 1059.0liquid fluid material being heated water water water water water waterfluid inlet temperature (deg. C.) 5 5 5 5 5 5 fluid density rho (g/cm3)0.9974 0.9974 0.9974 0.9974 0.9974 0.9974 fluid kinematic viscosity eta(g/cm- 9.80E−03 9.80E−03 9.80E−03 9.80E−03 9.80E−03 9.80E−03 sec) flowrate (liters/min) 2.50 2.50 2.50 2.50 2.50 2.50 flow rate (ml/sec) 41.6741.67 41.67 41.67 41.67 41.67 tubing flow cross section area (cm2)12.371 12.371 12.371 12.371 12.371 12.371 free stream velocity throughtubing 3.37 3.37 3.37 3.37 3.37 3.37 (cm/sec) Re = density * free stream1360 1360 1360 1360 1360 1360 vel. * hydraulic.diam/kinem. viscositynozzle ID friction factor (turbulent 0.0606 0.0606 0.0606 0.0606 0.06060.0606 flow - FIG. 6.4) pressure drop across tubing 0.34 0.40 0.45 0.510.63 0.74 (newtons/m2) Pascal pressure drop across tubing (psi) 0.000.00 0.00 0.00 0.00 0.00 fluid residence time at flow rate 11.73 13.6915.64 17.60 21.51 25.42 (secs) Prandtl No. Pr for water at 20 deg 6.786.78 6.78 6.78 6.78 6.78 C. = Cp * viscos/k (dimensionless) Nusselt No.Nu = 0.023Re{circumflex over ( )}0.8 * Pr{circumflex over ( )}0.4, 15.8915.89 15.89 15.89 15.89 15.89 turbulent flow thermal conductivity ofwater at 20 .00604 .00604 .00604 .00604 .00604 .00604 deg. C.watt/cm/deg C. heat transfer coefficient 0.02 0.02 0.02 0.02 0.02 0.02watt/cm2/deg. C. normalized film resis. (tube inner 41.347 41.347 41.34741.347 41.347 41.347 wall to water) (deg C./watt/cm2) tube inner surfacearea (cm2) 492.6 574.7 656.8 738.9 903.2 1067.4 tube outer surface area(cm2) 551.7 643.7 735.7 827.6 1011.5 1195.5 thermal resistance fromwater to tube .08393 .07194 .06295 .05595 .04578 .03874 inner surface(deg. C./watt) percent of total thermal resistance - 72% 72% 72% 72% 72%72% water to tube thickness of tube wall (cm) 0.238 0.238 0.238 0.2380.238 0.238 tubing material QRTZ QRTZ QRTZ QRTZ QRTZ QRTZ tube materialthermal conductivity 0.014 0.014 0.014 0.014 0.014 0.014 (watt/cm-deg.C.) normalized thermal resis. through the 17.01 17.01 17.01 17.01 17.0117.01 tube wall (deg C./watt/cm2) average area of tube wall (cm2) 522609 696 783 957 1,131 thermal resistance through the tube .03257 .02792.02443 .02171 .01777 .01503 wall (deg C./watt) percent of total thermalresistance - 28% 28% 28% 28% 28% 28% tube wall total thermal resistance(deg C./watt) .11650 .09986 .08738 .07767 .06355 .05377 total(normalized to ext. surf.) therm. 64.28 64.28 64.28 64.28 64.28 64.28resist.(deg C./watt/cm2) Transferred Power (watt) 5185 6049 6914 77789506 11235 Transferred Volume Power Density 11 11 11 11 11 11 (watt/cm3)mass flow rate of water (grams/sec) 42 42 42 42 42 42 heat capacity ofwater 4.179 4.179 4.179 4.179 4.179 4.179 Joules/gram/deg. C.temperature rise of water from inlet 29.86 34.83 39.81 44.78 54.74 64.69to outlet (deg. C.) Surface Power Density-Tube Exterior 9.40 9.40 9.409.40 9.40 9.40 Surface (watts/cm2) Surface Power Density-Tube 60.6360.63 60.63 60.63 60.63 60.63 Exterior (watts/in2) Aveage FluidTemperature (inlet and 17.43 19.92 22.40 24.89 29.87 34.84 outlet)Temp.Diff. to Transfer Specified 604.09 604.09 604.09 604.09 604.09604.09 Power (deg. C.) Avg. Element Temp. = Ext. Surf. 621.52 624.01626.50 628.99 633.96 638.94 Temp. to XFR Spec Pwr. (deg. C.) minimumelement temperature (deg. C.) 609.09 609.09 609.09 609.09 609.09 609.09maximum element temperature (deg. C.) 638.95 643.93 648.90 653.88 663.83673.78 outlet diss. ozone concentration/inlet 0.86 0.77 0.64 0.49 0.160.01 diss. ozone concentration

[0053] TABLE 13 Example 5 - Prior Art Design Prior Art Example for 5.0L/min flow tubing ID (inches) 1.5625 1.5625 1.5625 1.5625 1.5625 1.5625tubing OD (inches) 1.75 1.75 1.75 1.75 1.75 1.75 Inlet Temp T1 deg. C. 55 5 5 5 5 Outlet Temp T2 deg. C. 35 40 45 50 60 70 Req'd TemperatureRise deg. C. 30 35 40 45 55 65 Flow Rate L/min 5 5 5 5 5 5 Flow Rateml/sec 83.3 83.3 83.3 83.3 83.3 83.3 Reg'd Power kW 10.37 12.10 13.8315.56 19.01 22.47 Decay Constant Tau sec for given 79.4 52.9 35.7 24.311.7 5.9 ozone-water solution temp.T2 tubing ID (inches) 1.5625 1.56251.5625 1.5625 1.5625 1.5625 tubing OD (inches) 1.75 1.75 1.75 1.75 1.751.75 tubing wall thickness (inches) .09375 .09375 .09375 .09375 .09375.09375 tubing ID (cm) 3.969 3.969 3.969 3.969 3.969 3.969 tubing OD (cm)4.445 4.445 4.445 4.445 4.445 4.445 tubing wall thickness (cm) 0.2380.238 0.238 0.238 0.238 0.238 length of heated tube (in) scaled for31.11 36.30 41.48 46.67 57.04 67.41 given surf.pwr. densitylength of heated tube (ft) 2.59 3.02 3.46 3.89 4.75 5.62 length ofheated tube (cm) 79.0 92.2 105.4 118.5 144.9 171.2volume of heated tube (cm3) = ml 977.6 1140.5 1303.4 1466.3 1792.22118.1 liquid fluid material being heated water water water water waterwater fluid inlet temperature (deg. C.) 5 5 5 5 5 5 fluid density rho(g/cm3) 0.9974 0.9974 0.9974 0.9974 0.9974 0.9974 fluid kinematicviscosity eta (g/cm- 9.80E−03 9.80E−03 9.80E−03 9.80E−03 9.80E−039.80E−03 sec) flow rate (liters/min) 5.00 5.00 5.00 5.00 5.00 5.00 flowrate (ml/sec) 83.33 83.33 83.33 83.33 83.33 83.33 tubing flow crosssection area (cm2) 12.371 12.371 12.371 12.371 12.371 12.371 free streamvelocity through tubing 6.74 6.74 6.74 6.74 6.74 6.74 (cm/sec) Re =density * free stream 2721 2721 2721 2721 2721 2721 vel. *hydraulic.diam/kinem. viscosity nozzle ID friction factor (turbulent0.0470 0.0470 0.0470 0.0470 0.0470 0.0470 flow - FIG. 6.4) pressure dropacross tubing 2.12 2.47 2.83 3.18 3.89 4.59 (newtons/m2) Pascal pressuredrop across tubing (psi) 0.00 0.00 0.00 0.00 0.00 0.00fluid residence time at flow rate 11.73 13.69 15.64 17.60 21.51 25.42(secs) Prandtl No. Pr for water at 20 deg 6.78 6.78 6.78 6.78 6.78 6.78C. = Cp * viscos/k (dimensionless) Nusselt No. Nu = 0.023Re{circumflexover ( )}0.8 * Pr{circumflex over ( )}0.4, 27.67 27.67 27.67 27.67 27.6727.67 turbulent flow thermal conductivity of water at 20 .00604 .00604.00604 .00604 .00604 .00604 deg. C watt/cm/deg C. heat transfercoefficient 0.04 0.04 0.04 0.04 0.04 0.04 watt/cm2/deg. C. normalizedfilm resis. (tube inner 23.748 23.748 23.748 23.748 23.748 23.748 wallto water) (deg C./watt/cm2) tube inner surface area (cm2) 985.3 1149.51313.7 1477.9 1806.3 2134.7 tube outer surface area (cm2) 1103.5 1287.41471.3 1655.2 2023.1 2390.9 thermal resistance from water to tube .02410.02066 .01808 .01607 .01315 .01112 inner surface (deg. C./watt) percentof total thermal resistance - 60% 60% 60% 60% 60% 60% water to tubethickness of tube wall (cm) 0.238 0.238 0.238 0.238 0.238 0.238 tubingmaterial QRTZ QRTZ QRTZ QRTZ QRTZ QRTZ tube material thermalconductivity 0.014 0.014 0.014 0.014 0.014 0.014 (watt/cm-deg. C.)normalized thermal resis. through the 17.01 17.01 17.01 17.01 17.0117.01 tube wall (deg C./watt/cm2) average area of tube wall (cm2) 1,0441,218 1,393 1,567 1,915 2,263 thermal resistance through the tube 0.01620.0139 0.0122 0.0108 0.0088 0.0075 wall (deg C./watt) 9 6 1 6 8 2percent of total thermal resistance - 40% 40% 40% 40% 40% 40% tube walltotal thermal resistance (deg C./watt) 0.0403 0.0346 0.0302 0.02690.0220 0.0186 9 2 9 3 3 4 total (normalized to ext. surf.) therm. 44.5744.57 44.57 44.57 44.57 44.57 resist.(deg C./watt/cm2) Transferred Power(watt) 10370 12099 13827 15556 19012 22469 Transferred Volume PowerDensity 11 11 11 11 11 11 (watt/cm3) mass flow rate of water (grams/sec)83 83 83 83 83 83 heat capacity of water 4.179 4.179 4.179 4.179 4.1794.179 Joules/gram/deg. C. temperature rise of water from inlet 29.8634.83 39.81 44.78 54.74 64.69 to outlet (deg. C.) Surface PowerDensity - Tube Exterior 9.40 9.40 9.40 9.40 9.40 9.40 Surface(watts/cm2) Surface Power Density-Tube 60.63 60.63 60.63 60.63 60.6360.63 Exterior (watts/in2) Aveage Fluid Temperature (inlet and 17.4319.92 22.40 24.89 29.87 34.84 outlet) Temp.Diff. to Transfer Specified418.85 418.85 418.85 418.85 418.85 418.85 Power (deg. C.) Avg. ElementTemp. = Ext. Surf. 436.28 438.77 441.25 443.74 448.72 453.69 Temp. toXFR Spec Pwr. (deg. C.) minimum element temperature (deg. C.) 423.85423.85 423.85 423.85 423.85 423.85 maximum element temperature (deg. C.)453.71 458.68 463.66 468.63 478.59 488.54outlet diss. ozone concentration/inlet 0.86 0.77 0.64 0.49 0.16 0.01diss. ozone concentration

[0054] TABLE 14 Example 6 - Prior Art Design Prior Art Example for 10.0L/min flow tubing ID (inches) 1.5625 1.5625 1.5625 1.5625 1.5625 1.5625tubing OD (inches) 1.75 1.75 1.75 1.75 1.75 1.75 Inlet Temp T1 deg. C. 55 5 5 5 5 Outlet Temp T2 deg. C. 35 40 45 50 60 70Req'd Temperature Rise deg. C. 30 35 40 45 55 65 Flow Rate L/min 10 1010 10 10 10 Flow Rate ml/sec 166.7 166.7 166.7 166.7 166.7 166.7Req'd Power kW 20.74 24.20 27.65 31.11 38.02 44.94 Decay Constant Tausec for given 79.4 52.9 35.7 24.3 11.7 5.9 ozone-water solution temp.T2tubing ID (inches) 1.5625 1.5625 1.5625 1.5625 1.5625 1.5625 tubing OD(inches) 1.75 1.75 1.75 1.75 1.75 1.75 tubing wall thickness (inches)0.09375 0.09375 0.09375 0.09375 0.09375 0.09375 tubing ID (cm) 3.9693.969 3.969 3.969 3.969 3.969 tubing OD (cm) 4.445 4.445 4.445 4.4454.445 4.445 tubing wall thickness (cm) 0.238 0.238 0.238 0.238 0.2380.238 length of heated tube (in) scaled for 62.22 72.59 82.96 93.33114.07 134.81 given surf.pwr. density length of heated tube (ft) 5.196.05 6.91 7.78 9.51 11.23 length of heated tube (cm) 158.0 184.4 210.7237.1 289.7 342.4 volume of heated tube (cm3) =ml 1955.1 2281.0 2606.82932.7 3584.4 4236.1 liquid fluid material being heated water waterwater water water water fluid inlet temperature (deg. C.) 5 5 5 5 5 5fluid density rho (g/cm3) 0.9974 0.9974 0.9974 0.9974 0.9974 0.9974fluid kinematic viscosity eta (g/cm- 9.80E−03 9.80E−03 9.80E−03 9.80E−039.80E−03 9.80E−03 sec) flow rate (liters/min) 10.00 10.00 10.00 10.0010.00 10.00 flow rate (ml/sec) 166.67 166.67 166.67 166.67 166.67 166.67tubing flow cross section area (cm2) 12.371 12.371 12.371 12.371 12.37112.371 free stream velocity through tubing 13.47 13.47 13.47 13.47 13.4713.47 (cm/sec) Re = density * free stream 5442 5442 5442 5442 5442 5442vel. * hydraulic.diam/kinem. viscosity nozzle ID friction factor(turbulent 0.0376 0.0376 0.0376 0.0376 0.0376 0.0376 flow - FIG. 6.4)pressure drop across tubing 13.54 15.80 18.06 20.31 24.83 29.34(newtons/m2) Pascal pressure drop across tubing (psi) 0.00 0.00 0.000.00 0.00 0.00 fluid residence time at flow rate 11.73 13.69 15.64 17.6021.51 25.42 (secs) Prandtl No. Pr for water at 20 deg 6.78 6.78 6.786.78 6.78 6.78 C. = Cp * viscos/k (dimensionless) Nusselt No. Nu =0.023Re{circumflex over ( )}0.8 * Pr{circumflex over ( )}0.4, 48.1748.17 48.17 48.17 48.17 48.17 turbulent flow thermal conductivity ofwater at 20 .00604 .00604 .00604 .00604 .00604 .00604 deg. C.watt/cm/deg C. heat transfer coefficient 0.07 0.07 0.07 0.07 0.07 0.07watt/cm2/deg. C. normalized film resis. (tube inner 13.640 13.640 13.64013.640 13.640 13.640 wall to water) (deg C./watt/cm2) tube inner surfacearea (cm2) 1970.5 2298.9 2627.4 2955.8 3612.6 4269.5 tube outer surfacearea (cm2) 2207.0 2574.8 2942.7 3310.5 4046.1 4781.8 thermal resistancefrom water to tube .00692 .00593 .00519 .00461 .00378 .00319 innersurface (deg. C./watt) percent of total thermal resistance - 46% 46% 46%46% 46% 46% water to tube thickness of tube wall (cm) 0.238 0.238 0.2380.238 0.238 0.238 tubing material QRTZ QRTZ QRTZ QRTZ QRTZ QRTZ tubematerial thermal conductivity 0.014 0.014 0.014 0.014 0.014 0.014(watt/cm-deg. C.) normalized thermal resis. through the 17.01 17.0117.01 17.01 17.01 17.01 tube wall (deg C./watt/cm2) average area of tubewall (cm2) 2,089 2,437 2,785 3,133 3,829 4,526 thermal resistancethrough the tube .00814 .00698 .00611 .00543 .00444 .00376 wall (degC./watt) percent of total thermal resistance - 54% 54% 54% 54% 54% 54%tube wall total thermal resistance (deg C./watt) .01506 .01291 .01130.01004 .00822 .00695 total (normalized to ext. surf.) therm. 33.25 33.2533.25 33.25 33.25 33.25 resist.(deg C./watt/cm2) Transferred Power(watt) 20741 24198 27654 31111 38025 44938 Transferred Volume PowerDensity 11 11 11 11 11 11 (watt/cm3) mass flow rate of water (grams/sec)166 166 166 166 166 166 heat capacity of water 4.179 4.179 4.179 4.1794.179 4.179 Joules/gram/deg. C. temperature rise of water from inlet29.86 34.83 39.81 44.78 54.74 64.69 to outlet (deg. C.)Surface Power Density-Tube Exterior 9.40 9.40 9.40 9.40 9.40 9.40Surface (watts/cm2) Surface Power Density - Tube 60.63 60.63 60.63 60.6360.63 60.63 Exterior (watts/in2) Aveage Fluid Temperature (inlet and17.43 19.92 22.40 24.89 29.87 34.84 outlet) Temp.Diff. to TransferSpecified 312.46 312.46 312.46 312.46 312.46 312.46 Power (deg. C.) Avg.Element Temp. = Ext. Surf. 329.88 332.37 334.86 337.35 342.32 347.30Temp. to XFR Spec Pwr. (deg. C.) minimum element temperature (deg. C.)317.46 317.46 317.46 317.46 317.46 317.46maximum element temperature (deg. C.) 347.31 352.29 357.26 362.24 372.19382.14 outlet diss. ozone concentration/inlet 0.86 0.77 0.64 0.49 0.160.01 diss. ozone concentration

[0055] If we examine the inventive examples 1, 2, and 3 and compare themto the prior art design examples 4, 5, and 6 we note that the outletdissolved ozone concentration divided by the inlet dissolved ozoneconcentration is higher for the inventive design than for the prior artdesign and that the difference becomes more marked at higher heateroutlet temperatures. We have summarized the results for two outlettemperatures in table 15 below. We can see that the inventive heaterdesign example has the potential to supply a dissolved ozoneconcentration at the heater outlet at a temperature of 40 degree C. is27 percent higher than the prior art design; the inventive heater designexample has the potential to supply a dissolved ozone concentration atthe heater outlet at a temperature of 70 degree C. which is a factor of11 higher than the prior art design. This translates directly intoperformance improvements in systems employing the inventive heater toheat relatively low temperature ozone-water solutions (more generallyozone-solvent solutions) to higher temperatures to increase the surfacereaction rate while maintaining high dissolved ozone concentrations.Comparable differences between the inventive design and prior artdesigns are exhibited by the other inventive and prior art designexamples presented. TABLE 15 Heater Performance Comparison Prior ArtDesign Inventive Design Design Example 4 Example 1 Ozone-Solvent Soln.Temp. T1  @ 5 5 5 5 htr. inlet ° C. Ozone-Solvent Soln. Temp. T2  @ 4070 40 70 htr. oulet ° C. Outlet Diss. O3 Conc./Inlet Diss. .77 .06 .98.67 O3 Conc.

[0056] We can identify a number of important differences between theinventive design and the prior art design examples. First, the inventiveheater design examples have a much higher transferred volume powerdensity than the prior art design examples (˜112 watts/cm3 compared to11 watts/cm3). Second, the inventive heater design examples have a muchhigher internal surface area to internal volume ratio than the prior artdesign examples (5 cm-1 compared to 1 cm-1). This is summarized in thetable 16 below. TABLE 16 Heater Design Comparison Prior Art DesignInventive Design Design Example 4 Example 6 Example 1 Example 3Transferred Power 11 11 112 115 Density (watts/cm3) Internal SurfaceArea/ 1.0 1.0 8.76 5.0 Internal Volume (cm-1)

[0057] An inventive design with a transferred power density of as low as50 watts/cm3 will have a significant performance advantage over theprior art design examples shown, albeit not quite as dramatic as theinventive design examples shown. An inventive design with a surface tovolume ratio as low at 2.5 cm-1 will have a significant performanceadvantage over the prior art design examples shown, albeit not quite asdramatic as the inventive design examples shown.

[0058] The much higher transferred volume power density translates to amuch shorter residence time for a given transferred power and the muchhigher surface to volume ratio translates to lower thermal resistancesbetween the liquid and the interior wall for a given flow rate and lowerrequired exterior surface temperatures. Third, the inventive designexamples use smaller diameter heater tubes which can be constructed fromthinner walls for a given operating pressure. This translates into lowerthermal resistance between the interior wall and the exterior wall andlower required exterior surface temperatures. Additional differencesbetween the inventive design examples and the prior art design examplescan be noted by comparing the values for the other parameters shown inthe design examples.

[0059] The design examples shown above are representative of resistanceheated or induction heated designs and other designs in which power istransferred to a liquid flowing through a conduit by heating theexterior wall of the conduit. These design examples are alsorepresentative of many of the key features of heat exchanger inventivedesigns except the heat source is the heated working fluid flowing overthe exterior surface of the conduit in lieu of a heating element and thethermal resistance comprises the resistance from the process water tothe tube wall, the thermal resistance of the tube wall, and the thermalresistance from the tube wall to the working fluid. The inventive heatexchanger designs derive the same benefits from higher transferred powerdensities, higher surface to volume ratios, and smaller tube (conduit)diameters and exhibit similar advantages in performance over prior artdesigns except that the inventive heat exchanger designs with a multipletube in tube geometry, for use with tube materials with low thermalconductivity such as Teflon, have surface to volume ratios which are atleast a factor of two higher than the inventive resistance heated andinduction heated designs.

[0060] It should be noted that one can use similar approaches toincrease the surface to volume ratio for resistance heated and inductionheated designs which employ low thermal conductivity materials such asTeflon. These designs may employ an analog to the multiple tube-in-tubeheat exchanger design; such a design may employ, for example, sevensmall diameter Teflon coated heating elements inside a tube carrying thesolution to be heated. Other numbers of heating elements could be used,of course, but seven provides for a convenient close packed typestructure, with six elements spaced somewhat apart and surrounding aninner heating element, all surrounded by the outer tube.

[0061] The inventive heat exchanger designs have comparable transferredpower densities to those of the direct heater designs of the resistanceheated or induction heated type.

[0062] The inventive designs in which the flowing ozone-solvent solutionis heated by microwave radiation, infrared radiation, or heated fluidinjection derive the same benefit from a higher transferred powerdensity as the other inventive designs presented herein and use similarmaximum volumes and dimensions and are based upon the distinguishingdesign principles identified above. In the case of some of these designsone may achieve even higher transferred volume power densities. However,in these latter inventive designs, the power is not transferred by heatconduction through the conduit wall and from the wall through theflowing liquid boundary. In the microwave or infrared heated design theenergy is transferred by radiation through the tube wall. In the heatedfluid injection design using steam injection the energy is transferredwhen the injected steam releases its energy when it condenses.Accordingly the a high surface to volume ratio is not a critical elementof these latter designs. The designer may choose a convenient surface tovolume ratio provided that the geometry provides the high transferredpower density and other desired characteristics such as an acceptableflow induced pressure drop. In a single tube or multiple tube geometry,the use of a small tube diameter for high transferred volume powerdensity will also result in a relatively high surface to volume ratio.

[0063] The point-of-use heater is designed to have a small residencevolume so that the residence time between the cool ozone-water solutionentering the inlet of the heater and heated, supersaturated, ozone-watersolution reaches the point of application is small and there isinsufficient time for supersaturated solution to return to equilibriumbefore reaching the surface of the material to be oxidized. The timerequired for the solution to return to equilibrium is dependent upon thetemperature to which to solution is heated. Our preliminary measurementsindicate that at a temperature of about 50 degree C., a residence timeof 2 seconds will allow the dissolved concentration to only fall byabout 10 to 20 percent. At higher temperatures, the required residencetime is smaller. The residence time is proportional to the volume andinversely proportional to the dispense flow rate though that volume.

[0064] In collecting the data on the rate of decay of an ozone-watersolution as a function of the temperature of the ozone water solution,we prepared an ozone-water solution by dissolving ozone gas, atconcentration of 240 g/Nm3, a flow rate of 0.48 L/min, and a pressure of1 bar, into water at a temperature of about 8 degree C. using a MazzeiModel 287 venturi injector and bubble column contactor operated in therecirculating mode. We waited about 30 minutes and allowed the dissolvedconcentration to reach the saturation concentration at about 70. We drewthe ozone-water solution from the unpressurized contactor with a highpressure gear pump capable of delivering a flow rate of 2.7 L/minute at80 psi. We passed the solution through an Exergy tube in tube heatexchanger model 413, through a UV absorption type dissolved ozonemonitor and thermocouple probe, and then to a waste collection carboy.We measured the dissolved concentration upstream and downstream of theheater as a function of the temperature of the ozone-water solutiondownstream of the heater for several different temperatures. We usedthis data to estimate the decay time constant as function of temperatureby assuming that the decay time was an exponential function of thetemperature. We ran a similar test using coil in heated water bathheater. We flowed the water through a 20 foot long coil of stainlesssteel, 0.375 inch OD, 0.305 inch ID tubing, immersed in a heated waterbath. Since the water bath did not have sufficient power to maintain aconstant bath temperature, the dispense temperature of the ozone watersolution decreased about 5 degree C. during the test. Accordingly, weused average temperatures in analyzing the results. The residence volumeof the coil in bath heater was about 270 ml and the residence volume ofthe tube in tube heat exchanger was about 90 ml. (see the table 3footnotes) The results for both tests were consistent with the modelpresented below. The results for one test series are presented in Table17 below. TABLE 17 Decay time constant as a function of temperature:Measured decay time constant as function of temperature and calculateddecay time constant τ(Tau) as function of temperature assuming that thedecay time is an exponential function of the temperature τ = 2E−10 *Exp(8.26(1000/T) meas. calc. transit transit transit decay decay timetime time const. const. t decay t decay t decay Temp Temp. 1000/T τ τsecs factor secs factor secs factor deg. C. deg. K. (K) secs secs note 1exp(−t/τ) note 2 exp(−t/τ) note 3 exp(−t/τ) 20 293 3.41 292.3 2 99% 698% 22 93% 25 298 3.36 186.6 2 99% 6 97% 22 89% 30 303 3.30 120.9 2 98%6 95% 22 83% 35 308 3.25 79.4 2 98% 6 93% 22 76% 40 313 3.19 52.9 2 96%6 89% 22 66% 45 318 3.14 35.7 2 95% 6 85% 22 54% 50 323 3.10 24.3 2 92%6 78% 22 41% 55 328 3.05 16.8 2 89% 6 70% 22 27% 60 333 3.00 11.00 11.72 84% 6 60% 22 15% 65 338 2.96 8.4 8.3 2 79% 6 49% 22  7% 70 343 2.925.9 2 71% 6 36% 22  2% 75 348 2.87 4.05 4.3 2 63% 6 24% 22  1% 80 3532.83 3.1 2 52% 6 14% 22  0% 85 358 2.79 2.3 2 41% 6  7% 22  0% 90 3632.75 1.7 2 30% 6  3% 22  0% 95 368 2.72 1.3 2 20% 6  1% 22  0%

[0065] From this data we can see that higher temperatures cause theconcentration to fall more quickly. If one is to minimize the drop inconcentration upon heating, then the residence time must be decreased ifthe temperature is increased. For example, if we would like thedissolved ozone concentration at the outlet of the point-of-use heaterto be no less than 80 percent of the dissolved ozone concentration atthe inlet of the point-of-use heater, then the transit time must be lessthan or equal to the values estimated in Table 18 below. TABLE 18Maximum estimated permissible ozone-water solution heating time (heatertransit time): Calculated for the dissolved ozone concentration at theheater outlet to be no less than 80 percent of the dissolved ozoneconcentration at the heater inlet. Estimated from decay data measuredwith an inlet dissolved ozone concentration of about 100 mg/liter, aninitial upstream ozone-water solution temperature of about 8 deg. C. andthe a final specified downstream ozone-water solution temperatureranging from 20 deg. C. to 95 deg. C. Desired Decay Factor = 80%(Downstream Conc./Upstream Conc.) Estimated Calculated Ave solutiondecay maximum allowable temp. at heater const. heater transit timeoutlet Tau t = −τ*Ln(decay Temp Temp. τ factor) deg. C. deg. K 1000/T(K) secs secs 20 293 3.41 292.3 65.22  25 298 3.36 186.6 41.63  30 3033.30 120.9 26.97  35 308 3.25 79.4 17.72  40 313 3.19 52.9 11.80  45 3183.14 35.7 7.96 50 323 3.10 24.3 5.43 55 328 3.05 16.8 3.75 60 333 3.0011.7 2.62 65 338 2.96 8.3 1.85 70 343 2.92 5.9 1.32 75 348 2.87 4.3 0.9580 353 2.83 3.1 0.69 85 358 2.79 2.3 0.51 90 363 2.75 1.7 0.37 95 3682.72 1.3 0.28

[0066] If we return to the design examples shown above, we see thatanother important differenc between the new design shown under examples2, 3, and 4 and the conventional design that is the new design has aninternal volume of 50 to 100 ml whereas the conventional design has aninternal volume of 848 ml. At a flow rate of 2.65 L/min ˜45 ml persecond, an internal volume of 100 ml corresponds to a residence time of2.26 seconds and an internal volume of 848 ml corresponds to a residencetime of 19.2 seconds. This longer residence time impacts the decay ofthe ozone concentration as illustrated in Table 18 above.

[0067] Factors Determining Oxidation Rate or Removal Rate—A Model

[0068] The inventors have developed a model to help better understandthe factors determining oxidation and removal rate of an organicmaterial such as photoresist from a semiconductor wafer using anozone-solvent solution at concentration C and temperature T. The rate ofoxidation and removal of an organic layer from a substrate can bedefined in terms of an each rate can write an expression for the etchrate E (cm resist/sec) as E=C*(X/ρ)*(M*S)/(M+S). The parameter C (gozone/cm3) is the dissolved ozone the water far from the surface of theorganic layer on a semiconductor wafer bulk concentration). Theparameter X (g resist/g Ozone) is the mass of resist removed per mass ofozone consumed at the surface. The parameter p (g resist/cm3) is thedensity of the resist.

[0069] Dissolved Ozone Concentration C: When ozone is dissolved in asolvent, the maximum dissolved ozone concentration C that can beachieved after a sufficiently long transfer time, the saturationconcentration, is predicted by Henry's law. According to Henry's law,the maximum solubility is proportional to the partial pressure of theozone gas at a given temperature. Higher gas phase concentrations, highpressures, and lower solvent temperatures yield higher maximumequilibrium dissolved ozone concentrations.

[0070] We have calculated the approximate equilibrium saturationconcentration in mg/L (equivalent to parts per million by weight) for agas phase concentration of 240 mg/L (15.9 weight percent), pressures of1, 2, and 4 bar, and water (solvent) temperatures of 5 to 95 degree C.in 5 deg. C increments. See Table A. TABLE A Solubility of ozone gas inwater: The dissolved ozone concentration in mg/L as a function of thewater temperature and gas pressure for a gas phase ozone concentrationof 240 g/Nm3 = mg/liter (15.9 weight percent) in oxygen for a range ofwater temperatures. p = 1 bar p = 2 bar p = 4 bar (14.5 psia) (29 psia)(58 psia)  5 deg. C. 109 218 436 10 deg. C. 85 170 340 15 deg. C. 66 132264 20 deg. C. 52 104 208 25 deg. C. 40 80 160 30 deg. C. 31 62 124 40deg. C. 24 48 96 45 deg. C. 19 38 76 50 deg. C. 15 30 60 55 deg. C. 1122 44 60 deg. C. 9 18 36 65 deg. C. 7 14 28 70 deg. C. 5 10 20 75 deg.C. 4 8 16 80 deg. C. 3 6 12 85 deg. C. 2.5 5 10 90 deg. C. 1.2 2.4 4.895 deg. C. .9 1.8 3.6

[0071] Mass Transport Rate Coefficient M: The parameter M (cm/sec) isthe liquid phase mass transport rate coefficient. The ozone istransported to the wafer surface by diffusion. The mass transport rate M(cm/sec)=D/δ,where D (cm2/sec) is the diffusion constant of the ozonediffusing in the liquid and δ (cm) is the thickness of the stagnantlayer. The diffusion constant D for ozone in water is 1.7E-5 cm2/sec at20 deg. C. Accordingly the mass transport rate is increased when thediffusion constant is increased and/or the diffusion distance δ isdecreased.

[0072] Surface Reaction Rate Constant S: The parameter S(cm/sec) is thetemperature dependent surface reaction rate constant. The surfacereaction rate S (cm/sec) is an exponential function of the absolutetemperature T (deg. K) and the activation energy Ea of the oxidationprocess. In particular, S=Soexp(−Ea/KT) where K is Boltzman's constantand So is the surface reaction rate proportionality constant. Thedifference in etch rates of different materials at a given temperatureis attributed to the difference in the magnitude of the surface reactionrate constant for the two materials.

[0073] Etching Wafers at High Temperature: An increase in temperaturewill increase S and the magnitude of the term (M*S)/(M+S). If thedissolved concentration remained approximately constant with an increasein temperature, then we can see that the etch rate would increase withincreased temperature. However, as we have seen, the dissolved ozoneconcentration falls with increases in water temperature. If thetemperature is such that S>>M, the etch rate becomes mass transportlimited and E=C(X/ρ)*M. If M is larger, then the temperature at whichthe etch rate becomes limited by the mass transport rate M will behigher. If the temperature is higher, then the mass transport rate atwhich the etch rate will become mass transport limited will be higher.

[0074] Etching Wafers at Low Temperature: A decrease in temperature willdecrease S and the magnitude of the term (M*S)/(M+S). If the dissolvedconcentration remained approximately constant with decreases intemperature, then we can see that the etch rate would decrease with adecrease in temperature. However, as we have seen, the dissolved ozoneconcentration rises with decreases in water temperature. If thetemperature is decreased until S<<M, the etch rate becomes surfacereaction rate limited and E=C(X/ρ)*S.

[0075] An Approach to Achieving Very High Etch Rates: This model canprovide us valuable insight into the problem. It shows that thenormalized etch rate be increased by increasing the temperature and thatthe etch rate could be increased by increasing the temperature above 20degree C. if we could find a method to provide a higher dissolvedconcentration at the elevated temperature. The present preferredembodiments utilize just such a method.

[0076] The general principal is to achieve the highest dissolved ozoneconcentration at a given surface reaction temperature. This can be donein a number of ways including the following:

[0077] a) heat the cold ozone-solvent solution with an in-line heaterlocated just upstream of the point at which the ozone-solvent solutionis dispensed onto the substrate. The heated ozone-solvent solution willthen heat the surface of the substrate and increase the surface reactionrate. The ozone-solvent solution will retain most of the ozone dissolvedat the lower temperature if the solution is not heated until the lastmoment.

[0078] b) heat the cold ozone-solvent solution at the point ofapplication with a point of application heater as the solution passesover the substrate surface by for example using a radiant heater withthe wavelength band chosen to be absorbed by the ozone-solvent solution.The heated ozone-solvent solution will then heat the surface of thesubstrate and increase the surface reaction rate.

[0079] c) heat the substrate with a point of application heater anddispense the cold ozone-solvent solution onto the surface of the heatedsubstrate. Provide sufficient heat input to the substrate to overcomecooling effect of the cold solvent. In practice the substrate can beheated from the backside or from the front side. If the substrate isheated from the backside, the entire volume of the substrate may beheated so that the front surface, the surface to be etched, can beheated. If the substrate is heated from the front side, the entirevolume of the substrate may be heated or only the front surface may beheated. The surface reaction rate at the front surface is a function ofthe temperature of the front surface.

[0080] d) heat the cold ozone-solvent solution and heat the substrate byfor example using a radiant heater with the wavelength band chosen to beabsorbed partially by the ozone-solvent solution and partially by thesubstrate.

[0081] The substrate surface can be heated by conduction, convection, orradiation. The surface can be heated by conduction using a heatedsurface such as a hot plate. The surface can be heated by convectionusing a hot gas or hot liquid to the front or rear surface. Thesubstrate can be heated by radiation using a heat lamp or laser or othersource of radiation. The radiation wavelength band can be chosen so thatthe radiation passes through the ozone-water solution with little energydeposition in the water and the majority of the energy absorbed in thesurface. In fact the radiation can be chosen to be most stronglyabsorbed in the layer to removed (photoresist for example).

[0082] Teflon Heat Exchanger Design Calculation

[0083] Requirement: A heat exchanger with all Teflon PFA or Teflon PTFEwetted parts and a minimum internal volume (not to exceed 150 to 300 ml)and a tube flow rate of 1.65 to 3.3 Liter/minute. See Table 19. TABLE 19Teflon Exchanger Performance Requirement Inner Tubes Outer Tube (shell)Fluid Type water water Temp In ° C.  5 90 Temp Out ° C. 55 TBD TotalVolume Flow 2.0 L/min (1.65 to 3.3) TBD Pressure Drop TBD (not to exceedTBD (not to exceed 40 psi) 60 psi) Heat Transfer 6.9 kW for 2.0 L/minEffectiveness TBD Heat Transfer Coeff. TBD (W/m2 ° C.)

[0084] Design Approach: Since the thermal conductivity of Teflon is muchlower than stainless steel (0.22 compared to 16.3 watts/m2deg. K) theheat transfer area must be made larger by about a factor of 3 to 6. TheTube in Tube design is one approach. However, if we increase the lengthto 60 feet for a 0.25-inch OD inner tube design, the pressure dropincreases to a very high value. An alternative approach is a hybridbetween the 20-foot long tube in tube design and a 7-tube shell and tubedesign. In this case we can increase the heat transfer area by almost afactor of 3 for a given length. Since the Teflon is quite flexible thisshell & tube exchanger can be coiled in much the same manner as a tubein tube. A rough initial design is outlined in Table 20 below. Thelength and number of tubes should be adjusted to meet the requirement.The Teflon inner tubes can be connected at the inlet with a flarefitting approach at the exchanger end plates or by heat welding theTeflon inner tubes to Teflon End Plates. TABLE 20 Initial DesignParameters for a Proprietary Custom Shell &Tube Heat Exchanger withTeflon Inner Tubes Design: SHELL & TUBE outer tube (shell) materialTeflon PFA or 316 Stainless Steel inner tube material Teflon PFA PFAtubing surface roughness 1.7 RA (source Fluroware) PFA thermalConductivity 0.22 W/m2 deg. K outer tube (shell) OD 0.5 inches outertube (shell) ID 0.440 inches or 0.375 inches outer tube (shell) length =inner tube length inner tube OD 0.092 inches (similar dimension to anExergy 10 series shell and tube) inner tube wall thickness 0.008 inchesinner tube length ˜240 inches (TBD) number of inner tubes 7 heattransfer area (3120 cm2) inner tube volume (140 ml) out tube (shell)pressure drop at ˜60 psi (TBD) 2 L/min inner tube pressure drop @ 2 ˜10psi (TBD) L/min

[0085] TABLE 21 Example design parameters and calculated performance fordifferent process (inner tube) flow rates Process Flow Rate 1.65 L/min2.0 L/min 2.7 L/min 3.3 L/min outer tube material Teflon PFA Teflon PFATeflon PFA Teflon PFA or 316 SS or 316 SS or 316 SS or 316 SS innertubes material Teflon PTFE Teflon PTFE Teflon PTFE Teflon PTFE or PFA orPFA or PFA or PFA PFA tubing surface ˜1.7 RA ˜1.7 RA ˜1.7 RA ˜1.7 RAroughness PFA thermal Conductivity 0.22 0.22 0.22 0.22 (W/m2 deg. K)outer tube (shell) OD 0.5 0.5 0.5 0.5 (inches) outer tube (shell) ID(inches) 0.430 0.430 0.430 0.430 outer tube (shell) length inner tubeinner tube inner tube inner tube length length length length inner tubeOD 0.092 0.092 0.092 0.092 (inches) inner tube wall thickness 0.0080.008 0.008 0.008 (inches) number of inner tubes 7 7 7 7 inner tubelength (inches) 150 150 150 150 inner tube volume (ml) 82.2 82.2 82.282.2 available heat transfer area 1832 1832 1832 1832 (cm2) assumedeffective heat 1374 1374 1374 1374 transfer area (cm2) = see note 1inner tubes water water water water fluid type inner tubes 5 5 5 5 temp.in (deg. C.) inner tubes 63.8 57.9 48.7 42.9 temp out (deg. C.) innertubes 1.65 2.0 2.7 3.3 volume flow l/min inner tubes 27.3 33.1 44.7 54.6mass flow g/sec inner tubes pressure drop 12.5 17.5 29.5 41.9 (psi)outer tube water water water water fluid type outer tube 90 90 90 90temp. in (deg. C.) outer tube 83.4 82.8 82 81.5 temp out (deg. C.) outertube 14.9 14.9 14.9 14.9 volume flow l/min outer tube 242.9 242.9 242.9242.9 mass flow g/sec outer tube 45.1 45.1 45.1 45.1 pressure drop (psi)inner tube thermal 5281 6690 4647? conductivity (watts/deg. k) tube wallthermal 171 171 171 171 conductivity (watts/deg. k) outer tube thermal938 938 938 938 conductivity (watts/deg. k) inner tube .00019 .00015thermal resistance (deg. k/watt) tube wall .0058 .0058 .0058 .0058thermal resistance (deg. k/watt) outer tube .0011 .0011 .0011 .0011thermal resistance (deg. k/watt) total .0071 .0071 total thermalresistance (deg. k/watt) Heat Transfer (Btu/hr) 22903 21830 27842 29527Heat Transfer (watts) 6712 6398 8160 8653 Effectiveness .691 .659 .514.446

[0086] Key Design Elements: Direct Conduction Heated and Heat ExchangerDesigns

[0087] The Key Elements: Direct Conduction Heated Designs

[0088] 1. a heater based upon a small diameter tube has a higher surfacearea for a given volume

[0089] 2. a higher surface area decreases the thermal resistance betweenthe heated surface of the tube and the water in thermal contact with theother surface of the tube

[0090] 3. a lower thermal resistance decreases the temperaturedifference required to transfer given amount of power from the heatedsurface of the tube to the flowing water in thermal contact with theother surface of the tube

[0091] 4. a heater requiring a lower temperature difference between theheated surface of the tube and the water in thermal contact with theother surface of the tube requires a lower heated surface temperaturefor a given inlet and outlet water temperature.

[0092] 5. a heater based upon a small diameter tube has a smaller volumefor a given surface area and therefore a smaller residence time for agiven flow rate and given transferred power

[0093] 6. a heater based upon a small diameter tube of a given burstpressure rating may have a thinner wall than a larger diameter tube ofthe same burst pressure rating and correspondingly lower thermalresistance through the tube wall

[0094] 7. a heater based upon a small diameter tube has a higherreynolds number for a given flow rate and correspondingly lower thermalresistance between the water and the adjacent tube wall, i.e. the filmresistance is lower

[0095] 8. a heater based upon a small diameter tube has a smallerinternal volume and higher volume power density for a given powertransferred (eg. 100 watts/cm3) than a conventional heater which has avolume power density of the order of 10 watts/cm3

[0096] 9. a heater based upon multiple small diameter tubes with a giventotal cross sectional area has a higher surface area for a given volumethan a heater based upon a single small diameter tube with the samecross sectional area; such a heater will have a lower thermal resistanceand is a preferred geometry for tube materials of low thermalconductivity.

[0097] The Key Elements: Heat Exchanger Designs

[0098] 1. same as items 1-9 of the previous list except the heat sourceis the heated working fluid in lieu of a heating element and the thermalresistance comprises the resistance from the process water to the tubewall, the thermal resistance of the tube wall, and the thermalresistance from the tube wall to the working fluid.

[0099] Steam Heater Design Calculation

[0100] Process fluid heating using steam injection into anEductor—Technical Approach

[0101] The use of steam heaters for heating of liquids is well known tothose skilled in the art. Stream jet heaters optimize the condensing ofsteam into liquids to provide efficient fluid heating. Steam jet heatershave an inlet (sometimes called the motive flow inlet, the suctioninlet, and outlet. The process fluid in enters the motive flow inletunder pressure and travels through the nozzle into the suction chamber.The nozzle coverts the pressure of the process fluid entering the motiveflow inlet into a high velocity stream. The increase in velocity lowersthe pressure according to Bemolli's law. The steam which enters thesuction inlet is mixed with the process fluid. The steam condenses andreleases its heat of condensation into the process fluid and therebyheats the process fluid. If the pressure at the outlet is increasedabove a critical pressure, then the pressure at the “suction inlet” canrise above atmospheric pressure. In this case, the steam must beintroduced under pressure into the inlet.

[0102] The use of steam heaters for heating liquids has an additionaladvantage when used for quickly heating a supersaturated ozone-solventsolution. These heaters have a very small residence volume. Accordingly,they can quickly increase the temperature of a flowing ozone-solventsolution. A typical design is shown in Table 22 below. TABLE 22 Typicaldesign parameters for a steam heater design using an eductor or ejectorProcess Fluid Motive Flow Rate (L/min)  2.7 Motive Pressure 50 psigMotive Liquid Water (with ozone gas dissolved) Motive Liquid Temperature(deg. C.)  5 Motive Liquid Specific Gravity  1.0 Flow Rate into“Suction” port 0.5 lbs/min = .227 kgm/min Fluid into “Suction” portSaturated Steam (formed form ultra-pure Distilled Water) Fluid Pressureinto “Suction” port 25 psig. Outlet Pressure (psig) up to 50 psig.maximum Temperature Rise of Motive Liquid (deg. C.) 45 Temperature ofProcess Fluid at Outlet (deg. C.) 50 Eductor Make-Model-Size PenberthyModel HLM 1/2″, (cf = 0.047)

[0103] In most conventional applications, the eductor or ejector ismetal. In this application, where metal contamination must be avoided,the eductor or ejector may be fabricated with an alternative materialwhich is compatible with the process fluid and injected heated fluid(steam in this case) over the range of operating temperatures andpressures and does not introduce undesirable contaminants into theprocess fluid. Suitable materials in high purity applications include,but are not limited to, quartz and Teflon and Kynar (PVDF).

[0104] An alternative design for heating the process fluid with steam isto use a static mixer in lieu of an eductor or ejector. Static mixersare readily available in both metal and quartz.

[0105] The description of the preferred embodiments for apparatus forquickly heating a flowing ozone-solvent solution is divided into fourgroups of figures:

[0106] 1st GROUP: Direct Conduction Heater Designs (FIG. 1 & FIG. 2)

[0107] 2^(nd) GROUP: Heat Exchanger Designs (FIG. 3 & FIG. 4)

[0108] 3^(rd) GROUP: Direct Microwave Heater Designs (FIG. 5)

[0109] 4th GROUP: Direct Infrared Heater Designs (FIG. 6)

[0110] 5th GROUP: Heated Fluid Injection Designs (FIG. 7)

[0111] 6^(th) GROUP: Long Heater Design Geometry (FIG. 8 and FIG. 9)

[0112] FIGS. 1-9 are not drawn to scale. With reference to FIGS. 1-9,the tube or conduit(s) which carries the process fluid or are contactedby the process fluid, may be made from any material which is compatiblewith the process fluid over the range of operating temperatures andpressures and does not introduce undesirable contaminants into theprocess fluid. Suitable materials in high purity applications include,but are not limited to, quartz, Teflon, stainless steel, and titanium.In some applications it is desirable to exclude metals from the wettedmaterials. In these cases materials such as quartz and Teflon arepreferred materials of construction. In some applications in whichheating elements are deposited on the exterior surface of the wettedmaterials, insulating materials or metal materials covered by aninsulating film are preferred. Let us now continue our discussion ofinventive heater designs. It should be understood that the designdiscussions and quantitative data present earlier are still relevant tothe inventive designs. The supplement the design examples sketched inFIGS. 1 through 9 and provide the basis of a number of designssummarized in table form above. We do not provide figures of all theembodiments mentioned in table summary form, but only show one or twoexamples to illustrate the family of designs that are contemplated inthis specification. In all the designs presented here, the liquid isconveyed to and from the heater with suitable sections of processcompatible tubing or conduit (not shown). The inlet and outlet of theheater are connected to the tubing with suitable flare type,compression, or other fittings. The length and inside diameter of thetubing from the heater outlet to the point of use is chosen to have asmall volume since any added volume increases the effective residencevolume through which the heated solution must flow from the point ofheating to the point of use. This residence volume determines theresidence time and the ratio of the outlet dissolved ozone concentrationto the inlet dissolved ozone concentration as discussed earlier.

[0113] 1st GROUP: Direct Conduction Heater Designs (FIG. 1 & FIG. 2)

[0114] An apparatus for quickly heating a flowing ozone-solvent solutiontemperature from a relatively low temperature T1 to a relatively hightemperature T2 using a direct conduction heater. A number of embodimentsare described above and two are illustrated in FIG. 1 and FIG. 2.

[0115]Fig. 1a—Single Tube Solution-Heater with Resistance HeatedElements on Outside of Tube—Longitudinal Heating Element(s).

[0116] Description and Operation Fig. 1a

[0117] With reference to Fig 1 a, a heating element 22 is formed on theexterior surface of a quartz tube 24. The heating element may bedeposited in a serpentine pattern over the exterior surface of the tubeas shown in FIG. 1a. A suitable electrical connection pad can beprovided at each end of the heater element. One connection pad 26 isvisible in the figure and the other connection pad is hidden from view.In some cases it may be desirable to form more than one heating elementon the surface of the heater. A relatively low temperature ozone-watersolution, ozone-solvent solution, or other liquid flows into inlet 28 ofthe quartz heater tube at a given flow rate and then exits from theoutlet 30 at the higher temperature. The flow direction for the fluidentering and leaving the heater is shown by the flow arrows 32 and 34. Atemperature sensor and controller (not shown) detects the outlet liquidtemperature and controls the application of power to the leads of theheater. The controller compares the actual temperature to the setpointand controls power to the heater to bring the temperature of the flowingliquid at the outlet to the setpoint temperature. The liquid is conveyedto and from the heater with suitable sections of process compatibletubing or conduit (not shown). The inlet and outlet of the heater areconnected to the tubing with suitable flare type, compression, or otherfittings. The length and inside diameter of the tubing from the heateroutlet to the point of use is chosen to have a small volume since anyadded volume increases the effective residence volume through which theheated solution must flow from the point of heating to the point of use.This residence volume determines the residence time as discussedearlier. It is often desirable to fabricate multiple heaters usingrelatively short sections of tubing (12 to 36 inches for example) andthen joining those sections together in series or in parallel withTeflon compression tube fittings, or other suitable fittings, to formheaters with higher power capacity. A series connection of threesections is shown in FIG. 8 that follows later in this discussion. Theheat power supply may be single phase or three phase. In many high powerapplications, three phase power is convenient. If each heater has onlyone heating element, then a heater system assembled comprising threeheated tubing sections or multiples of three sections can beconveniently connected to a three phase power source and present abalanced load.

[0118] With reference to FIG. 1a, a first method of forming the heatingelement is to utilize a foil electric heating circuit that is placeddirectly in thermal contact with the surface of the tubular or othershaped conduit that carries the process fluid to be heated. The foilcircuit may be formed by etching, die punching, cutting, or similarlyknown processes. Such foil electric circuits are known in the heaterindustry.

[0119] With reference to FIG. 1a, a second method of forming the heatingelement is to use a thick film deposition material such as electricallyconductive or resistive inks or pastes or epoxies which may be screenprinted, dispensed, or painted directly onto the surface of the tubeother shaped conduit that carries the process fluid to be heated. Suchthick film pastes or inks are supplied by a number of companiesincluding Electro-Science Laboratories.

[0120] With reference to FIG. 1, a third method of forming the heatingelement is to from a thin film heating element by a thin film depositionprocess such as sputtering, chemical vapor deposition, vacuumevaporation, or other thin film deposition process

[0121]Fig. 1b—Single Tube Solution-heater with Resistance HeatedElements on Outside of Tube —Spiral Heating Element(s).

[0122] Description and Operation Fig. 1b

[0123] With reference to Fig 1 b, a heating element 36 is formed on theexterior surface of a quartz tube 38. The heating element may bedeposited in a spiral over the exterior surface of the tube as shown inFIG. 1b. A suitable electrical connection pad can be provided at eachend of the heater element. One connection pad 40 is at one end of thetube and the other connection pad 42 is at the opposite end of theheater tube. In some cases it may be desirable to form more than oneheating element on the surface of the heat. A relatively low temperatureozone-water solution, ozone-solvent solution, or other liquid flows intoinlet 44 of the quartz heater tube at a given flow rate and then exitsfrom the outlet 46 at the higher temperature. The flow direction for thefluid entering and leaving the heater is shown by the flow arrrows 48and 50. A temperature sensor and controller (not shown) detects theoutlet liquid temperature and controls the application of power to theleads of the heater. The controller compares the actual temperature tothe setpoint and controls power to the heater to bring the temperatureof the flowing liquid at the outlet to the setpoint temperature. Theflow direction for the fluid entering and leaving the heater is shown bythe flow arrows 60 and 62. The liquid is conveyed to and from the heaterwith suitable sections of process compatible tubing or conduit (notshown). The inlet and outlet of the heater are connected to the tubingwith suitable flare type, compression, or other fittings. The length andinside diameter of the tubing from the heater outlet to the point of useis chosen to have a small volume since any added volume increases theeffective residence volume through which the heated solution must flowfrom the point of heating to the point of use. This residence volumedetermines the residence time as discussed earlier. It is oftendesirable to fabricate multiple heaters using relatively short sectionsof tubing (12 to 36 inches for example) and then joining those sectionstogether in series or in parallel with Teflon compression tube fittings,or other suitable fittings, to form heaters with higher power capacity.A series connection of three sections is shown in FIG. 8 that followslater in this discussion. The heat power supply may be single phase orthree phase. In many high power applications, three phase power isconvenient. If each heater has only one heating element, then a heatersystem assembled comprising three heated tubing sections or multiples ofthree sections can be conveniently connected to a three phase powersource and present a balanced load.

[0124] With reference to FIG. 1b, a first method of forming the heatingelement is to utilize a foil electric heating circuit that is placeddirectly in thermal contact with the surface of the tubular or othershaped conduit that carries the process fluid to be heated. The foilcircuit may be formed by etching, die punching, cutting, or similarlyknown processes. Such foil electric circuits are known in the heaterindustry.

[0125] With reference to FIG. 1b, a second method of forming the heatingelement is to use a thick film deposition material such as electricallyconductive or resistive inks or pastes or epoxies which may be screenprinted, dispensed, or painted directly onto the surface of the tubeother shaped conduit that carries the process fluid to be heated. (Aconvenient method of applying the spiral pattern is to dispense the inkor paste from a nozzle which is moved in the longitudinal direction asthe tube is slowly rotated about its longitudinal axis.) Such thick filmpastes or inks are supplied by a number of companies includingElectro-Science Laboratories. In the case of relatively small diametertubes (for example 0.250 to 0.375 inch), a spiral pattern may easier toapply than a longitudinal pattern such as that shown in FIG. 1a.

[0126] With reference to FIG. 1b, a third method of forming the heatingelement is to from a thin film heating element by a thin film depositionprocess such as sputtering, chemical vapor deposition, vacuumevaporation, or other thin film deposition process.

[0127] A first alternative inventive design to that shown in FIG. 1a or1 b is a single tube-in-tube resistance heated design employing a tubewithin a tube with resistive heating elements in thermal contact withthe outer surface of the outer tube. The fluid to be heated (processfluid) flows through the volume between the outer tube and the innertube. (Figure not shown.)

[0128] A second alternative design to that shown in FIGS. 1a or 1 b is asingle tube-in-tube resistance heated design employing a tube withintube with resistive heating elements in thermal contact with the outersurface of the outer tube and resistive heating elements in thermalcontact with the inner surface of the inner tube. The fluid to be heated(process fluid) flows through the volume between the outer tube and theinner tube. (Figure not shown.)

[0129] A third alternative design to that shown in FIGS. 1a or 1 b is amultiple tube-in-tube resistance heated design employing an outer tubeand a multiplicity of inner tubes with resistive heating elements inthermal contact with the inner surfaces of the inner tubes The fluid tobe heated (process fluid) flows through the volume between the outertube and the multiplicity of inner tubes. (Figure not shown.)

[0130]FIG. 2—Single Tube Solution-heater with Induction Heated Elementson Outside of Tube.

[0131] Description and Operation—FIG. 2

[0132] With reference to FIG. 2, an inductively heated element 52 isformed on the exterior surface of a quartz tube 54. The heating elementmay be deposited in a uniform pattern over the exterior surface of thetube as shown in FIG. 2. A relatively low temperature ozone-watersolution, ozone-solvent solution, or other liquid flows into inlet 56 ofthe quartz heater tube at a given flow rate and then exits from theoutlet 58 at the higher temperature. The flow direction for the fluidentering and leaving the heater is shown by the flow arrows 60 and 62. Atemperature sensor and controller (not shown) detects the outlet liquidtemperature and controls the application of power to the solenoid shapedinduction coil which surrounds the heater (not shown). The controllercompares the actual temperature to the setpoint and controls power tothe induction heating coil which controls the magnitude of the currents(eddy currents) induced in the heating element to bring the temperatureof the flowing liquid at the outlet to the setpoint temperature. Theliquid is conveyed to and from the heater with suitable sections ofprocess compatible tubing or conduit (not shown). The inlet and outletof the heater are connected to the tubing with suitable flare type,compression, or other fittings. The length and inside diameter of thetubing from the heater outlet to the point of use is chosen to have asmall volume since any added volume increases the effective residencevolume through which the heated solution must flow from the point ofheating to the point of use. This residence volume determines theresidence time as discussed earlier. It is often desirable to fabricatemultiple heaters using relatively short sections of tubing (12 to 36inches for example) and then joining those sections together in seriesor in parallel with Teflon compression tube fittings, or other suitablefittings, to form heaters with higher power capacity. A seriesconnection of three sections is shown in FIG. 8 that follows later inthis discussion. The heat power supply may be single phase or threephase. In many high power applications, three phase power is convenient.If each heater has only one heating element, then a heater systemassembled comprising three heated tubing sections or multiples of threesections can be conveniently connected to a three phase power source andpresent a balanced load.

[0133] With reference to FIG. 2, a first method of forming the inductionheating element is to utilize a foil electric heating element that isplaced directly in thermal contact with the surface of the tubular orother shaped conduit that carries the process fluid to be heated. Thefoil element may be formed by etching, die punching, cutting, orsimilarly known processes.

[0134] With reference to FIG. 2, a second method of forming theinduction heating element is to use a thick film deposition materialsuch as electrically conductive or resistive inks or pastes or epoxieswhich may be screen printed, dispensed, or painted directly onto thesurface of the tube other shaped conduit that carries the process fluidto be heated. Such thick film pastes or inks are supplied by a number ofcompanies including Electro-Science Laboratories.

[0135] With reference to FIG. 2, a third method of forming the inductionheating element is to from a thin film heating element by a thin filmdeposition process such as sputtering, chemical vapor deposition, vacuumevaporation, or other thin film deposition process.

[0136] A first alternative inventive design to that shown in FIG. 2 is asingle tube-in-tube induction heated design employing a tube withinductively heated elements in thermal contact with the outer surface ofthe outer tube. The fluid to be heated (process fluid) flows through thevolume between the outer tube and the inner tube. (Figure not shown.)

[0137] A second alternative inventive design to that shown in FIG. 2 isa single tube-in-tube induction heated design employing an outer tubeand inner tube with inductively heated elements in thermal contact withthe outer surface of the outer tube and inductively heated elements inthermal contact with the inner surface of the inner tube. The fluid tobe heated (process fluid) flows through the volume between the outertube and the inner tube. (Figure not shown.)

[0138] A third alternative inventive design to that shown in FIG. 2 is amultiple tube-in-tube induction heated design employing an outer tubeand a multiplicity of inner tubes with inductively heated elements inthermal contact with the inner surfaces of the inner tubes The fluid tobe heated (process fluid) flows through the volume between the outertube and the multiplicity of inner tubes. (Figure not shown.)

[0139] Since the induction heating element can be a film deposited in anun-broken film on the outer surface of the quartz tube, the heat istransferred uniformly to the outer surface

[0140] 2nd GROUP: Heat Exchanger Designs (FIG. 3 & FIG. 4)

[0141] The tube(s) which carries the process fluid, may be made from anymaterial which is compatible with the process fluid over the range ofoperating temperatures and pressures and does not introduce undesirablecontaminants into the process fluid. Suitable materials in high purityapplications include, but are not limited to, quartz and Teflon. Thetube(s) which carries the working fluid, may be made from any materialwhich is compatible with the working fluid over the range of operatingtemperatures and pressures. Suitable materials include, but are notlimited to, stainless steel, titanium, copper, aluminum, Quartz, andTeflon. Many applications in semiconductor processing may employ quartzor Teflon and in some cases titanium or titanium alloys, aluminum oraluminum alloys, and other selected non-ferrous metals and non-ferrousmetal alloys.

[0142]FIG. 3—A single Tube-in-tube Heat Exchanger with Process FluidFlowing Through the Inner Tube.

[0143] Description and Operation—FIG. 3

[0144] With reference to FIG. 3, a typical tube-in-tube heat exchangergeometry is shown. A relatively low temperature ozone-water solution,ozone-solvent solution, or other liquid flows into inlet 64 of the innerat a given flow rate and then exits from the outlet 66. The flowdirection for the fluid entering and leaving the heater is shown by theflow arrows 68 and 70. The inner tube 72 is surrounded by a largerdiameter outer tube 74. The outer tube has an inlet port 76 at one endand outlet port 78 at the other end. A heated working fluid, typicallysupplied by a heating recirculator, enters inlet port 76 and exits fromoutlet port 78. The hot working fluid flows along longitudinal axis ofthe heater in the annular volume between the inner tube 72 and the outertube 74. The flow direction of the hot working fluid is counter to theflow direction of the process fluid being heated. The flow direction forthe hot working fluid entering and leaving the heat exchanger is shownby the flow arrows 80 and 82. The outer tube of the heat exchanger hasend covers 84 and 86, through which the inner tube 74 passes. Thisarrangement can be achieved by welding in case of metal exchangermaterials, by heat fusing in the case of quartz heat exchangermaterials, and or by the use of suitable fittings to form separateconnections to the inlet and outlets for each side of the exchanger inthe case of Teflon heat exchanger designs. The hot working fluid, hotwater in many applications, heats the exterior surface of the inner tube72. The power transferred through the wall of the inner tube to heat theprocess fluid that enters inlet 64 is determined by the averagetemperature differential and the thermal resistance between the hotworking fluid and the process fluid as discussed in the analysis sectionon direct conduction heated designs. However, in the case of heatexchangers, the working fluid temperature is typically lower than theheating element temperature in a direct conduction heated design heater.In the case of water as a working fluid, the maximum temperature is 85to 90 degree C. In contast, heating element temperatures may be 150 to200 degree C. or higher. Accordingly, a lower thermal resistance isrequired to transfer the same power in a heat exchanger since thetemperature difference is lower. A first alternative design (not shown)is a single tube-in-tube heat exchanger with the fluid to be heated(process fluid) flowing in the volume between the outer tube and theinner tube and a heated fluid (working fluid) flowing through the innertube.

[0145]FIG. 4—A multiple Tube-in-tube Heat Exchanger with Process FluidFlowing Through the Inner Tubes.

[0146] Description and Operation—FIG. 4

[0147] If a heat exchanger is fabricated from metal, then a single tubein tube design can provide an sufficiently low thermal resistance toachieve good power transfer for these modest temperature differences.However, if the heat exchanger is fabricated from Teflon, then a newinventive design, the multiple tube in tube design, is preferred. Thisinventive design is actually a hybrid of the shell in tube design and asingle tube in tube design. The use of multiple tubes in lieu of asingle tube increases the surface area for heat transfer and therebydecreases the thermal resistance such that materials other than metal,such as Teflon or quartz may be employed despite their lower thermalconductivity as discussed in the earlier design analysis.

[0148] With reference to FIG. 4, the inventive multiple tube-in-tubeheat exchanger geometry is shown. A multiplicity of inner tubes 88 issurrounded by a larger diameter outer tube 90. In the design exampleshown there are seven inner tubes arranged in a hexagonal array. Theouter tube of the heat exchanger has an outlet end fitting 92 andsimilarly designed inlet end fitting (not shown). The outlet end fittinghas seven tubing connectors 94 which are connected through anintervening manifold volume 96 to a single outlet tube 98. The seventubing connections connect to the outlet ends of the seven smalldiameter inner tubes. The inlet end fitting is of the same design andconnects the a single inlet tube (not shown) to the inlets of the sevensmall diameter inner tubes. The tubing connections may be welded orfused joints or hose fittings.

[0149] A relatively low temperature ozone-water solution, ozone-solventsolution, or other liquid flows into inlet tube of the inlet end fitting(not shown) to feed the inlets of the seven small diameter tubes 88. Theflow passes through the inner tubes to the outlet end fitting 92 to theoutlet fitting 98. The flow direction for the fluid entering and leavingthe heater is shown by the flow arrows 100 and 102.

[0150] A heated working fluid, typically supplied by a heatingrecirculator, enters inlet port 104 and exits from outlet port 106. Thehot working fluid flows along longitudinal axis of the heater in theinterstitial volume between the seven inner tubes 88 and the outer tube90. The flow direction of the hot working fluid is counter to the flowdirection of the process fluid being heated. The flow direction for thehot working fluid entering and leaving the heat exchanger is shown bythe flow arrows 108 and 110.

[0151] The outer tube of the heat exchanger has an outlet end fitting 95and an inlet end fitting of the same design (not shown). These fittingscan be fabricated by welding in case of metal exchanger materials, byheat fusing in the case of quartz heat exchanger materials, and or bythe use of suitable fittings and a fabricated transition piece tobetween the seven the small end fittings and the single inlet or outletfitting.

[0152] In practice for the flow rates and power levels listed in theanalysis of the direct conduction heated designs, a tube in tubeexchanger may have an outer diameter of the order of 0.5 inch and alength of the order of 10 to 20 feet. The analysis of the multipletube-in-tube heat exchanger with Teflon wetted materials was presentedin any earlier discussion. FIG. 4, like all the other figures, is not toscale; the heater is much longer relative to its diameter than depicted.

[0153] A first alternative design (not shown) is a multiple tube-in-tubeheat exchanger with fluid to be heated (process fluid) flowing in theannular volume between the outer tube and the multiplicity of innertubes and the heated fluid (working fluid) flowing through the innertubes.

[0154] 3^(rd) GROUP: Direct Microwave Heater Designs (FIG. 5)

[0155]FIG. 5—Single Tube Solution-heater with a Microwave RadiationSource to Heat the Liquid Flowing in the Tube.

[0156] Description and Operation—FIG. 5

[0157] With reference to FIG. 5, the inventive direct microwave heaterdesign is shown. A length of quartz tubing 112 is contained inside amicrowave resonator 114. Microwave resonator 114 is connected tomicrowave power source 116 by a length of wave-guide 119. A relativelylow temperature ozone-water solution, ozone-solvent solution, or otherliquid flows into inlet 118 of the quartz tube 112 at a given flow rateand then exits from the outlet 120 at the higher temperature. The flowdirection for the fluid entering and leaving the microwave heater isshown by the flow arrows 122 and 124.

[0158] A temperature sensor and controller (not shown) detects theoutlet liquid temperature and controls the application of microwavepower to the flowing liquid. The controller compares the actualtemperature to the setpoint and controls power to bring the temperatureof the flowing liquid at the outlet to the setpoint temperature.

[0159] 4th GROUP: Direct Infrared Heater Designs (FIG. 6)

[0160]FIG. 6—Single Tube Solution-heater with a Infrared RadiationSource to Heat the Liquid Flowing in the Tube.

[0161] Description and Operation—FIG. 6

[0162] With reference to FIG. 6, the inventive direct infrared heaterdesign is shown. A relatively low temperature ozone-water solution,ozone-solvent solution, or other liquid flows into inlet 126 of thequartz tube 128 at a given flow rate and then exits from the outlet 130at the higher temperature. The flow direction for the fluid entering andleaving the infrared heater is shown by the flow arrows 132 and 134. Twoinfrared radiation sources 136 and 138 are positioned adjacent to thequartz tube. Two shaped reflectors 140 and 142 reflect the infraredradiation toward the quartz tube. The inner surfaces 144 and 146 of thereflectors are coated with suitable infrared reflecting layers.

[0163] A temperature sensor and controller (not shown) detects theoutlet liquid temperature and controls the application of infrared powerto the flowing liquid. The controller compares the actual temperature tothe setpoint and controls power to bring the temperature of the flowingliquid at the outlet to the setpoint temperature.

[0164] 5th GROUP: Heated Fluid Injection Designs (FIG. 7)

[0165]FIG. 7—A Fluid Injection Type Heater with a Heated Fluid (HeatedWater or Steam for Example) Injected into the Inlet Port of an Injectorand the Fluid to be Heated (Cold Process Fluid) Flowing into the MotiveFlow Inlet of the Injector and the Heated Process Fluid Flowing from theOutlet Port of the Injector.

[0166] Description and Operation—FIG. 7

[0167] With reference to FIG. 7, the inventive fluid injection heaterdesign is shown in a block diagram. A relatively low temperatureozone-water solution, ozone-solvent solution, or other liquid (theprocess fluid) flows into inlet motive flow inlet port of an eductor,ejector, or venturi injector 150 and exits from the outlet port 152 atthe higher temperature. A source of water 154 feeds the inlet 156 ofsteam generator 158. The outlet of the steam generator 158 is connectedby a conduit to the suction inlet (mixing) port of the eductor, ejector,or venturi injector 150. The steam injected mixes with the process fluidinside the injector and condenses. When the steam condenses, its givesup energy (its heat of condensation) to the process fluid and increasesthe temperature of the process fluid. Given that an injector can have avery small internal volume of less than 20 ml, the residence time isvery small and the process fluid (an ozone solvent solution for example)can be heated very rapidly.

[0168] The tube and injector element which carries both the processfluid and the injected heated fluid (high purity steam for example), maybe made from any material which is compatible with the process fluid andinjected heated fluid over the range of operating temperatures andpressures and does not introduce undesirable contaminants into theprocess fluid. Suitable materials in high purity applications include,but are not limited to, quartz and Teflon.

[0169] A first alternative inventive design may employ a static mixer inlieu of a venturi injector, eductor, or ejector. Static mixers arereadily available in quartz.

[0170] 6th GROUP: Long Heater Design Geometry FIG. 8 and FIG. 9)

[0171]FIG. 8—A General Approach to Joining Individual Straight Sectionsof Heater with Fittings into a Folded Compact Heater Design.

[0172] Description and Operation—FIG. 8

[0173] It is often desirable to fabricate multiple heaters usingrelatively short sections of tubing (12 to 36 inches for example) andthen joining those sections together in series or in parallel withTeflon compression tube fittings, or other suitable fittings, to formheaters with higher power capacity. A series connection of threesections is shown in FIG. 8 that follows later in this discussion. Theheat power supply may be single phase or three phase. In many high powerapplications, three phase power is convenient. If each heater has onlyone heating element, then a heater system assembled comprising threeheated tubing sections or multiples of three sections can beconveniently connected to a three phase power source and present abalanced load.

[0174] In reference to FIG. 9, three short heater sections 162, 164, and166 are joined in series by U-bends 168 and 170 and tubing connectors172, 174, 176, and 178. The connectors may be Teflon compression tubefittings. The process fluid then enters the inlet 180 of the firstsection 162, and flows through the connected sections 164 and 166 to theoutlet 182. In practice any number of heaters can be interconnected inthis manner. If each heater section is sized for 1 kW power transfer,then nine heaters can be interconnected in this way to form a compact3×3 array of parallel heater tubes for a total heating capacity of 9 kW.Such an array can be conveniently connected to a three phase powersource as discussed above.

[0175]FIG. 9—A General Approach to Bending a Long Heater into a Coil fora Compact Heater Design.

[0176] Description and Operation—FIG. 9

[0177] An alternative approach to fabricating long direct heated heatersor heat exchangers is to bend a long heater into a coil as shownschematically in FIG. 9. This is particularly attractive for themultiple tube in tube heater based upon inner tubes of Teflon which andan outer tube of Teflon or Stainless Steel. A 10 to 20 foot longmultiple tube in tube heat exchanger can be very compact in a coiledconfiguration.

[0178] Other Considerations

[0179] Those skilled in the art will appreciate that the presentinvention, and the inventions described in the referenced priorapplication Ser. No. 09/693,012, can be extended to other gas-solventsolutions. In particular the invention can be extended to hydrogen-watersolutions and other hydrogen-solvent solutions. One can, for example,form a hydrogen-water solution at a relatively low temperature T1 toform a relatively high dissolved hydrogen concentration, and thenquickly heat the hydrogen-solvent solution to a relatively hightemperature T2 to form a hydrogen water solution with a much highersurface reaction rate at temperature T2 than an hydrogen-water solutionat T1, and with a much higher dissolved hydrogen concentration attemperature T2 than could be achieved if the hydrogen-water solution hadoriginally been formed at T2. Hydrogen-water solutions and otherhydrogen solvent solutions are important in the processing of materialsand electronic devices because they are reducing agents. One applicationmay be the rapid re-hydrogenation of ion-implanted photoresist tofacilitate removal. Those skilled in the art will appreciate thatalthough the present invention can be extended to Hydrogen-solventsolutions, there are some significant differences due to the fact thatthe Hydrogen does not tend to decompose as does ozone when subjected toa rising temperature.

1. A method of quickly heating an ozone-solvent solution from arelatively low temperature T1 to a relatively high temperature T2, suchthat said ozone-solvent solution has a much higher dissolved ozoneconcentration at temperature T2 than could be achieved if theozone-solvent solution had originally been formed at said temperatureT2, comprising: a) introducing said ozone-solvent solution at atemperature T1 into a heating volume, said heating volume also having anoutlet orifice; b) transferring sufficient power into said heatingvolume while said ozone-solvent solution is flowing through said heatingvolume to create a heated flowing ozone-solvent solution having atemperature T2 at the outlet orifice of the heating volume, c) receivingsaid heated flowing ozone-solvent solution at said temperature T2 fromthe outlet orifice of said heating volume.
 2. The method of claim 1wherein the power transferred has a power density greater than 20 w/cm3.3. The method of claim wherein the power transferred has a power densitygreater than 50 w/cm3.
 4. The method of claim 1 wherein the powertransferred has a power density greater than 100 w/cm3.
 5. The method ofclaims 1, 2, 3, or 4 wherein the heating volume is contained by anon-metallic material.
 6. The method of claim 5 wherein the non-metallicmaterial is selected from the group consisting of Teflon PFA, TeflonTFE, Teflon PTFE, PVDF, quartz, glass, plastic, ceramic, Aluminum Oxide,and Aluminum Nitride.
 7. The method of claim 1, 2, 3, or 4 wherein theheating volume is contained by a non-ferrous metal or a non-ferrousmetal.
 8. The method of claims 1, 2, 3, or 4 wherein the heating volumeis contained by a non-ferrous metal or non-ferrous metal alloy selectedfrom the group consisting of aluminum, aluminum alloys, titanium, andtitanium alloys.
 9. The method of claim 5 wherein said heating volume iscontained by an internal surface area and wherein the ratio of thatinternal surface area to the heating volume is at least 2.5 cm-1. 10.The method of claim 6 wherein said heating volume is contained by aninternal surface area and wherein the ratio of that internal surfacearea to the heating volume is at least 2.5 cm-1.
 11. The method of claim7 wherein said heating volume is contained by an internal surface areaand wherein the ratio of that internal surface area to the heatingvolume is at least 2.5 cm-1.
 12. The method of claim 8 wherein saidheating volume is contained by an internal surface area and wherein theratio of that internal surface area to the heating volume is at least2.5 cm-1.
 13. The method of claim 1 wherein said heating volume iscontained by an internal surface area and wherein said power istransferred into said heating volume by resistance heated elements inthermal contact with said surface area.
 14. The method of claim 1wherein said heating volume is contained by an internal surface area andwherein said power is transferred into said heating by induction heatedelements in thermal contact with said surface area.
 15. The method ofclaim 1 wherein said heating volume is contained by an internal surfacearea and wherein said power is transferred into said heating volume by aheated fluid in thermal contact with said surface area.
 16. The methodof claim 1 wherein said power is transferred from a microwave powersource to the flowing ozone solvent solution.
 17. The method of claim 1the power is transferred from an infrared power source to the flowingozone solvent solution.
 18. The method of claim 1 wherein the power istransferred by mixing a heated fluid with the flowing ozone solventsolution.
 19. The method of claim 18 wherein the heated fluid comprisessteam.
 20. The method of claim 1 wherein said heating volume iscontained by an internal surface area and wherein the ratio of thatinternal surface area to the heating volume is at least 2.0 cm-1. 21.The method of claim 1 wherein said heating volume is contained by aninternal surface area and wherein the ratio of that internal surfacearea to the heating volume is at least 5.0 cm-1.
 22. A device forquickly heating a flowing ozone-solvent solution from a relatively lowtemperature T1 to a relatively high temperature T2 to form anozone-solvent solution with a much high dissolved ozone concentration attemperature T2 than could be achieved if the ozone-solvent solution hadoriginally been formed at T2 comprising: a) A solution heating volumewith an inlet for receiving a flowing ozone-solvent solution at atemperature T1 and an outlet for delivering said ozone-solvent solution;b) power means for transferring power to said ozone solvent solution assaid ozone-solvent solution flows from said inlet, through said solutionheating volume, to said outlet.
 23. A device as in claim 22 wherein saidpower means provides a power density greater than 20 w/cm3 to saidflowing ozone-solvent solution.
 24. A device as in claim 22 wherein saidpower means provides a power density greater than 50 w/cm3 to saidflowing ozone-solvent solution.
 25. A device as in claim 22 wherein saidpower means provides a power density greater than 20 w/cm3 to saidflowing ozone-solvent solution.
 26. A device as in claim 22 wherein saidsolution heating volume is contained by an internal surface, and whereinsaid power means comprises resistance heated elements in thermal contactwith said internal surface.
 27. A device as in claim 22 wherein saidsolution heating volume is contained by an internal surface, and whereinsaid power means comprises induction heated elements in thermal contactwith said internal surface.
 28. A device as in claim 22 wherein saidsolution heating volume is contained by an internal surface, and whereinsaid power means comprises a heated fluid in thermal contact with saidinternal surface.
 28. A device as in claim 22 wherein said power meanscomprises a microwave power source coupled to a resonant cavity at leastpartially enclosing the solution heating volume.
 29. A device as inclaim 22 wherein said power means comprises an infrared power sourcewhich illuminates the flowing ozone solvent solution as it passesthrough the solution heating volume.
 30. A device as in claim 22 whereinsaid power means comprises a source of heated fluid coupled to aninjector directed so as to mix said heated fluid with the flowing ozonesolvent solution.
 31. A device as in claim 30 wherein said heated fluidcomprises steam.
 32. A device as in claim 22 wherein said solutionheating volume is contained by an internal surface, and wherein theratio of the area of the internal surface to the volume of said solutionheating volume is at least 2.0 cm-1.
 33. A device as in claim 22 whereinsaid solution heating volume is contained by an internal surface, andwherein the ratio of the area of the internal surface to the volume ofsaid solution heating volume is at least 5.0 cm-1.